@article{ab13
,author    = "Abdulle, A. and Blumenthal, A."
,title     = "Stabilized multilevel {M}onte {C}arlo method
              for stiff stochastic differential equations"
,journal   = "Journal of Computational Physics"
,volume    = "251"
,pages     = "445-460"
,year      = 2013
}

@incollection{ab15
,author    = "Abdulle, A. and Blumenthal, A."
,title     = "Improved stabilized multilevel {M}onte {C}arlo method
              for stiff stochastic differential equations"
,series    = "Lecture Notes in Computational Science and Engineering"
,volume    = "103"
,publisher = "Springer"
,pages     = "537-545"
,year      = 2015
}

@article{abs13
,author    = "Abdulle, A. and Barth, A. and Schwab, C."
,title     = "Multilevel {M}onte {C}arlo methods for 
              stochastic elliptic multiscale {PDE}s"
,journal   = "Multiscale Modeling and Simulation"
,volume    = "11"
,number    = "4"
,pages     = "1033-1070"
,year      = 2013
}

@article{abs13
,author    = "Abdulle, A. and Barth, A. and Schwab, C."
,title     = "Multilevel {M}onte {C}arlo methods for 
              stochastic elliptic multiscale {PDE}s"
,journal   = "Multiscale Modeling and Simulation"
,volume    = "11"
,number    = "4"
,pages     = "1033-1070"
,year      = 2013
}

@article{ak14
,author    = "Alaya, M.B. and Kebaier, A."
,title     = "Multilevel {M}onte {C}arlo for {A}sian options and limit theorems"
,journal   = "Monte Carlo Methods and Applications"
,volume    = "20"
,number    = "3"
,pages     = "181-194"
,year      = 2014
}

@article{ak15
,author    = "Alaya, M.B. and Kebaier, A."
,title     = "Central limit theorem for the multilevel
              {M}onte {C}arlo {E}uler method"
,journal   = "Annals of Applied Probability"
,volume    = "25"
,number    = "1"
,pages     = "211-234"
,year      = 2015
}

@article{ahk16
,author    = "Alaya, M.B. and Hajji, K. and Kebaier, A."
,title     = "Importance sampling and statistical {R}omberg method
              for {L}{\'e}vy processes"
,journal   = "Stochastic Processes and their Applications"
,volume    = "126"
,number    = "7"
,pages     = "1901-1931"
,year      = 2016
}

@article{auh17
,author    = "Ali, A.A. and Ullmann, E. and Hinze, M."
,title     = "Multilevel {M}onte {C}arlo analysis for optimal control of
              elliptic {PDE}s with random coefficients"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "5"
,number    = "1"
,pages     = "466-492"
,year      = 2017
}

@article{ab16
,author    = "Alkhatib, A. and Babael, M."
,title     = "Applying the multilevel {M}onte {C}arlo method for
              heterogeneity-induced uncertainty quantification of
              surfactant/polymer flooding"
,journal   = "SPE Journal"
,volume    = "21"
,number    = "4"
,year      = "2016"
}

@article{an15
,author    = "Altmayer, M. and Neuenkirch, A."
,title     = "Multilevel {M}onte {C}arlo quadrature of discontinuous
              payoffs in the generalized {H}eston model using
              {M}alliavin integration by parts"
,journal   = "SIAM Journal on Financial Mathematics"
,volume    = "6"
,number    = "1"
,pages     = "22–52"
,year      = "2015"
}

@article{as14
,author    = "Alzubaidi, H. and Shardlow, T."
,title     = "Improved simulation techniques for first exit time
              of neural diffusion models"
,journal   = "Communications in Statistics - Simulation and Computation"
,volume    = "43"
,number    = "10"
,pages     = "2508-2520"
,year      = "2014"
}

@article{ah12
,author    = "Anderson, D. and Higham, D.J."
,title     = "Multi-level {M}onte {C}arlo for continuous time {M}arkov
              chains, with applications in biochemical kinetics"
,journal   = "SIAM Multiscale Modelling and Simulation"
,volume    = "10"
,number    = "1"
,pages     = "146-179"
,year      = "2012"
}

@article{ahs14
,author    = "Anderson, D. and Higham, D.J. and Sun, Y."
,title     = "Complexity of multilevel {M}onte {C}arlo tau-leaping"
,journal   = "SIAM Journal of Numerical Analysis"
,volume    = "52"
,number    = "6"
,pages     = "3106-3127"
,year      = "2014"
}

@article{ahs16
,author    = "Anderson, D. and Higham, D.J. and Sun, Y."
,title     = "Multilevel {M}onte {C}arlo for stochastic differential
              equations with small noise"
,journal   = "SIAM Journal of Numerical Analysis"
,volume    = "54"
,number    = "2"
,pages     = "505-529"
,year      = "2016"
}

@article{ak17
,author    = "Anderson, P. and Kohatsu-Higa, A."
,title     = "Unbiased simulation of stochastic differential equations
              using parametrix expansion"
,journal   = "Bernoulli"
,volume    = "23"
,number    = "3"
,pages     = "2028-2057"
,year      = "2017"
}

@article{anv17
,author    = "Aslett, L.J.M. and Nagapetyan, T. and Vollmer, S.J."
,title     = "Multilevel {M}onte {C}arlo for reliability theory"
,journal   = "Reliability Engineering \& System Safety"
,volume    = "165"
,pages     = "188-196"
,year      = "2017"
}

@article{avikainen09
,author    = "Avikainen, R."
,title     = "On irregular functionals of {SDEs} and the {E}uler scheme"
,journal   = "Finance and Stochastics"
,volume    = "13"
,number    = "3"
,pages     = "381-401"
,year      = "2009"
}

@article{bg14
,author    = "Baldeaux, J. and Gnewuch, M."
,title     = "Optimal randomized multilevel algorithms for
              infinite-dimensional integration on function
              spaces with {ANOVA}-type decomposition"
,journal   = "SIAM Journal of Numerical Analysis"
,volume    = "52"
,number    = "3"
,pages     = "1128-1155"
,year      = 2014
}

@article{bsz11
,author    = "Barth, A. and Schwab, C. and Zollinger, N."
,title     = "Multi-level {M}onte {C}arlo finite element method for
              elliptic {PDE}s with stochastic coefficients"
,journal   = "Numerische Mathematik"
,volume    = "119"
,number    = "1"
,pages     = "123-161"
,year      = 2011
}

@article{bl12
,author    = "Barth, A. and Lang, A."
,title     = "Multilevel {M}onte {C}arlo method with applications
              to stochastic partial differential equations"
,journal   = "Int.~Journal of Computer Mathematics"
,volume    = "89"
,number    = "18"
,pages     = "2479-2498"
,year      = "2012"
}

@article{bls13
,author    = "Barth, A. and Lang, A. and Schwab, C."
,title     = "Multilevel {M}onte {C}arlo method for parabolic
              stochastic partial differential equations"
,journal   = "BIT Numerical Mathematics"
,volume    = "53"
,number    = "1"
,pages     = "3-27"
,year      = "2013"
}

@article{bht20
,author    = "Bayer, C. and Ben Hammouda, C. and Tempone, R."
,title     = "Multilevel {M}onte {C}arlo combined with numerical smoothing for
              robust and efficient option pricing and density estimation"
,journal   = "ArXiv preprint: 2003.05708"
,year      = "2020"
}

@article{bfrs16
,author    = "Bayer, C. and Friz, P.K. and Riedel, S. and Schoenmakers, J."
,title     = "Complexity of multilevel {M}onte {C}arlo tau-leaping"
,journal   = "SIAM Journal of Numerical Analysis"
,volume    = "54"
,number    = "3"
,pages     = "1449-1483"
,year      = "2016"
}

@article{bdn15
,author    = "Belomestny, D. and Dickmann, F. and Nagapetyan, T."
,title     = "Pricing Bermudan options via multilevel approximation methods"
,journal   = "SIAM Journal of Financial Mathematics"
,volume    = "6"
,number    = "1"
,pages     = "448-466"
,year      = "2015"
}

@article{bs13
,author    = "Belomestny, D. and Schoenmakers, J. and Dickmann, F."
,title     = "Multilevel dual approach for pricing {A}merican style
              derivatives"
,journal   = "Finance and Stochastics"
,volume    = "17"
,number    = "4"
,pages     = "717-742"
,year      = "2013"
}

@article{bn17
,author    = "Belomestny, D. and Nagapetyan, T."
,title     = "Multilevel path simulation for weak approximation schemes
              with application to {L\'e}vy-driven {SDE}s"
,journal   = "Bernoulli"
,volume    = "23"
,number    = "2"
,pages     = "927-950"
,year      = "2017"
}

@article{bmt17
,author    = "Ben Hammouda, C. and Moraes, A. and Tempone, R."
,title     = "Multilevel hybrid split-step implicit tau-leap"
,journal   = "Numerical Algorithms"
,volume    = "74"
,number    = "2"
,pages     = "527-560"
,year      = "2017"
}

@article{bjltz16
,author    = "Beskos, A. and Jasra, A. and Law, K.J.H. and Tempone, R.
              and Zhou, Y."
,title     = "Multilevel sequential {M}onte {C}arlo samplers"
,journal   = "Stochastic Processes and their Applications"
,year      = "2016"
}

@article{bc15
,author    = "Bierig, C. and Chernov, A."
,title     = "Convergence analysis of multilevel {M}onte {C}arlo variance
              estimators and application for random obstacle problems"
,journal   = "Numerische Mathematik"
,volume    = "130"
,number    = "4"
,pages     = "579-613"
,year      = "2015"
}

@article{bc16
,author    = "Bierig, C. and Chernov, A."
,title     = "Approximation of probability density functions by the
              multilevel {M}onte {C}arlo {M}aximum {E}ntropy method"
,journal   = "Journal of Computational Physics"
,volume    = "314"
,pages     = "661-681"
,year      = "2016"
}

@incollection{bg15
,author    = "Blanchet, J.H. and Glynn, P.W."
,title     = "Unbiased {M}onte {C}arlo for optimization and functions of
              expectations via multilevel randomization"
,booktitle = "Proceedings of the 2015 Winter Simulation Conference"
,publisher = "IEEE"
,year      = "2015"
}

@article{bgr94
,author    = "Brandt, A. and Galun, M. and Ron, D."
,title     = "Optimal multigrid algorithms for calculating
              thermodynamic limits"
,journal   = "Journal of Statistical Physics"
,volume    = "74"
,number    = "1-2"
,pages     = "313-348"
,year      = 1994
}

@article{bi03
,author    = "Brandt, A. and Ilyin, V."
,title     = "Multilevel {M}onte {C}arlo methods for studying large
              scale phenomena in fluids"
,journal   = "Journal of Molecular Liquids"
,volume    = "105"
,number    = "2-3"
,pages     = "245-248"
,year      = 2003
}

@incollection{bswohrkk14
,author    = "Brugger, C. and de Schryver, C. and Wehn, N. and
              Omland, S. and Hefter, M. and Ritter, K. and 
              Kostiuk, A. and Korn, R."
,title     = "Mixed Precision Multilevel {M}onte {C}arlo
              on Hybrid Computing Systems"
,booktitle = "Proceedings of the Conference on Computational
              Intelligence for Financial Engineering and Economics"
,publisher = "IEEE"
,year      = "2014"
}

@article{br12
,author    = "Bujok, K. and Reisinger, C."
,title     = "Numerical valuation of basket credit derivatives
              in structural jump-diffusion models"
,journal   = "Journal of Computational Finance"
,volume    = "15"
,number    = "4"
,pages     = "115-158"
,year      = "2012"
}

@article{bhr15
,author    = "Bujok, K. and Hambly, B. and Reisinger, C."
,title     = "Multilevel simulation of functionals of
              {B}ernoulli random variables with application
              to basket credit derivatives"
,journal   = "Methodology and Computing in Applied Probability"
,volume    = "17"
,number    = "3"
,pages     = "579-604"
,year      = "2015"
}

@phdthesis{burgos14
,author    = "Burgos, S."
,title     = "The computation of {G}reeks with
              multilevel {M}onte {C}arlo"
,school    = "University of Oxford"
,type      = "{DPhil} thesis"
,year      = "2014"
}

@incollection{bg12
,author    = "Burgos, S. and Giles, M.B."
,title     = "Computing {G}reeks using multilevel path simulation"
,publisher = "Springer"
,pages     = "281-296"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2010"
,editor    = "Plaskota, L. and Wo{\'z}niakowski, H."
,year      = "2012"
}

@incollection{bdkkshk14
,author    = "Butler, R. and Dodwell, T.J. and Kim, T. and
              Kynaston, S. and Scheichl, R. and Haftka, R.T. and Kim, N.H."
,title     = "Uncertainty quantification of composite structures
              with defects using multilevel {M}onte {C}arlo simulations"
,booktitle = "Proceedings of the 17th Non-Deterministic Approaches Conference"
,publisher = "AIAA"
,year      = "2014"
}

@article{chjz22
,author    = "Chada, N.K. and Hoel, H. and Jasra, A. and Zouraris, G.E."
,title     = "Improved efficiency of multilevel {M}onte {C}arlo for stochastic
              {PDE} through strong pairwise coupling"
,journal   = "Journal of Scientific Computing"
,volume    = "93"
,number    = "3"
,pages     = "63"
,year      = "2022"
}

@article{cst13
,author    = "Charrier, J. and Scheichl, R. and Teckentrup, A."
,title     = "Finite element error analysis of elliptic {PDE}s
              with random coefficients and its application to 
              multilevel {M}onte {C}arlo methods"
,journal   = "SIAM Journal on Numerical Analysis"
,volume    = "51"
,number    = "1"
,pages     = "322-352"
,year      = "2013"
}

@article{ch12
,author    = "Chen, N. and Huang, Z."
,title     = "Brownian meanders, importance sampling and unbiased
              simulation of diffusion extremes"
,journal   = "Operations Research Letters"
,volume    = "40"
,number    = "6"
,pages     = "554-563"
,year      = "2012"
}

@booklet{cl12
,author    = "Chen, N. and Liu, Y."
,title     = "Estimating expectations of functionals of conditional
              expected via multilevel nested simulation"
,howpublished = "Presentation at conference on {M}onte {C}arlo
                 and {Q}uasi-{M}onte {C}arlo {M}ethods, {S}ydney"
,year      = "2012"
}

@article{cgst11
,author    = "Cliffe, K.A. and Giles, M.B. and Scheichl, R. and Teckentrup, A."
,title     = "Multilevel {M}onte {C}arlo methods and applications to
              elliptic {PDE}s with random coefficients"
,journal   = "Computing and Visualization in Science"
,volume    = "14"
,number    = "1"
,pages     = "3-15"
,year      = "2011"
}

@article{cf25
,author    = "Cornalba, F. and Fischer, J."
,title     = "Multilevel {M}onte {C}arlo methods for the {D}ean-{K}awasaki
              equation from fluctuating hydrodynamics"
,journal   = "SIAM Journal on Numerical Analysis"
,volume    = "63"
,number    = "1"
,pages     = "262-287"
,year      = "2025"
}

@article{chnst15
,author    = "Collier, N. and Haji-Ali, A.-L. and Nobile, F. 
              and von Schwerin, E. and Tempone, R."
,title     = "A Continuation Multilevel {M}onte {C}arlo algorithm"
,journal   = "BIT Numerical Mathematics"
,volume    = "55"
,number    = "2"
,pages     = "399-432"
,year      = "2015"
}

@article{cdmr09
,author    = "Creutzig, J. and Dereich, S. and
              M{\"u}ller-Gronbach, T. and Ritter, K."
,title     = "Infinite-dimensional quadrature and approximation of distributions"
,journal   = "Foundations of Computational Mathematics"
,volume    = 9
,number    = 4
,pages     = "391-429"
,year      = 2009
}

@article{cgrf18
,author    = "Croci, M. and Giles, M.B. and Rognes, M.E. and Farrell, P.E."
,title     = "Efficient white noise sampling and coupling for multilevel
              {M}onte {C}arlo with non-nested meshes"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = 6
,number    = 4
,pages     = "1630-1655"
,year      = 2018
}

@article{cgf21
,author    = "Croci, M. and Giles, M.B. and Farrell, P.E."
,title     = "Multilevel quasi {M}onte {C}arlo methods for elliptic {PDE}s
              with random field coefficients via fast white noise sampling"
,journal   = "SIAM Journal on Scientific Computing"
,volume    = 43
,number    = 4
,pages     = "A2480-A2868"
,year      = 2021
}

@article{dang17
,author    = "Dang, D.-M."
,title     = "A multi-level dimension reduction {M}onte-{C}arlo method
              for jump–diffusion models"
,journal   = "Journal of Computational and Applied Mathematics"
,volume    = "324"
,pages     = "49-71"
,year      = 2017
}

@incollection{dh13
,author    = "Daun, T. and Heinrich, S."
,title     = "Complexity of {B}anach space valued and parametric integration"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2012"
,editor    = "Dick, J. and Kuo, F.Y. and Peters, G.W. and Sloan, I.H."
,pages     = "297-316"
,year      = "2013"
}

@article{dh14a
,author    = "Daun, T. and Heinrich, S."
,title     = "Complexity of parametric initial value problems in {B}anach spaces"
,journal   = "Journal of Complexity"
,volume    = 30
,number    = 4
,pages     = "392-429"
,year      = "2014"
}

@article{dh14b
,author    = "Daun, T. and Heinrich, S."
,title     = "Complexity of parametric integration in various smoothness classes"
,journal   = "Journal of Complexity"
,volume    = 30
,number    = 6
,pages     = "750-766"
,year      = "2014"
}

@article{dh17
,author    = "Daun, T. and Heinrich, S."
,title     = "Complexity of {B}anach space valued and parametric
              stochastic It{\^o} integration"
,journal   = "Journal of Complexity"
,volume    = "40"
,pages     = "100-122"
,year      = "2017"
}

@article{dr15
,author    = "Debrabant, K. and R{\"o}{\ss}ler, A."
,title     = "On the acceleration of the multi-level {M}onte {C}arlo method"
,journal   = "Journal of Applied Probability"
,volume    = 52
,number    = 2
,pages     = "307-322"
,year      = 2015
}

@article{djl17
,author    = "Del Moral, P. and Jasra, A. and Law, K.J.H."
,title     = "Multilevel sequential {M}onte {C}arlo: {M}ean
              square error bounds under verifiable conditions"
,journal   = "Stochastic Analysis and Applications"
,volume    = 35
,number    = 3
,pages     = "478-498"
,year      = 2017
}

@article{dh11
,author    = "Dereich, S. and Heidenreich, F."
,title     = "A multilevel {M}onte {C}arlo algorithm for {L\'e}vy-driven
              stochastic differential equations"
,journal   = "Stochastic Processes and their Applications"
,volume    = 121
,number    = 7
,pages     = "1565-1587"
,year      = 2011
}

@article{dns12
,author    = "Dereich, S. and Neuenkirch, A. and Szpruch, L."
,title     = "An {E}uler-type method for the strong approximation
             of the {C}ox--{I}ngersoll--{R}oss process"
,journal   = "Proc.~Roy.~Soc.~A"
,volume    = 468
,number    = 2140
,pages     = "1105-1115"
,year      = 2012
}

@article{dereich11
,author    = "Dereich, S."
,title     = "Multilevel {M}onte {C}arlo algorithm for {L\'e}vy-driven
             {SDE}s with {G}aussian correction"
,journal   = "Annals of Applied Probability"
,volume    = 21
,number    = 1
,pages     = "283-311"
,year      = 2011
}

@article{dl16
,author    = "Dereich, S. and Li, S."
,title     = "Multilevel {M}onte {C}arlo algorithm for {L\'e}vy-driven
             {SDE}s: central limit theorems for adaptive {E}uler schemes"
,journal   = "Annals of Applied Probability"
,volume    = 26
,number    = 1
,pages     = "136-185"
,year      = 2016
}

@incollection{dl16b
,author    = "Dereich, S. and Li, S."
,title     = "Multilevel {M}onte {C}arlo implementation for {SDE}s
              driven by truncated stable processes"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2014"
,editor    = "Cools, R. and Nuyens, D."
,year      = "2016"
}

@article{dg14a
,author    = "Dick, J. and Gnewuch, M."
,title     = "Infinite-dimensional integration in weighted {H}ilbert
              spaces: anchored decompositions, optimal deterministic
              algorithms, and higher order convergence"
,journal   = "Foundations of Computational Mathematics"
,volume    = 14
,number    = 5
,pages     = "1027-1077"
,year      = 2014
}

@article{dg14b
,author    = "Dick, J. and Gnewuch, M."
,title     = "Optimal randomized changing dimension algorithms
              for infinite-dimensional integration on function
              spaces with {ANOVA}-type decomposition"
,journal   = "Journal of Approximation Theory"
,volume    = "184"
,pages     = "111-145"
,year      = 2014
}

@article{ds16
,author    = "Dickmann, F. and Schweizer, N."
,title     = "Faster comparison of stopping times by nested
              conditional {M}onte {C}arlo"
,journal   = "Journal of Computational Finance"
,volume    = "20"
,number    = "2"
,pages     = "101-123"
,year      = 2016
}

@article{dccrr13
,author    = "Dimits, A.M. and Cohen, B.I. and Caflisch, R.
              and Rosin, M.S. and Ricketson, L.F."
,title     = "Higher-order time integration of {C}oulomb collisions
              in a plasma using {L}angevin equations"
,journal   = "Journal of Computational Physics"
,volume    = "242"
,pages     = "561-580"
,year      = 2013
}

@article{dkst15
,author    = "Dodwell, T.J. and Ketelsen, C. and Scheichl, R. and
              Teckentrup, A.L."
,title     = "A hierarchical multilevel {M}arkov {C}hain {M}onte
              {C}arlo algorithm with applications to uncertainty
              quantification in subsurface flow"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    =  3
,number    = "1"
,pages     = "1075–1108"
,year      = "2015"
}

@booklet{dbs25
,author    = "Djurdjevac, A. and Bris, C.L. and S{\"u}li, E."
,title     = "A nonnegativity-preserving finite element method for a class
              of parabolic {SPDE}s with multiplicative noise"
,howpublished = "arXiv preprint arXiv:2502.16854"
,year         = "2025"
}

@article{eik13
,author    = "Efendiev, Y. and Iliev, O. and Kronsbein, C."
,title     = "Multilevel {M}onte {C}arlo methods using ensemble level 
              mixed {MsFEM} for two-phase flow and transport simulations"
,journal   = "Computational Geosciences"
,volume    = "17"
,number    = "5"
,pages     = "833-850"
,year      = 2013
}

@article{ejpt15
,author    = "Efendiev, Y. and Jin, B. and Presho, M. and Tan, X."
,title     = "Multilevel {M}arkov {C}hain {M}onte {C}arlo method for
              high-contrast single-phase flow problems"
,journal   = "Communications in Computational Physics"
,volume    = "17"
,number    = "1"
,pages     = "259-286"
,year      = 2015
}

@article{ekl15
,author    = "Efendiev, Y. and Kronsbein, C. and Legoll, F."
,title     = "Multilevel {M}onte {C}arlo
              approaches for numerical homogenization"
,journal   = "Multiscale Modeling \& Simulation"
,volume    = "13"
,number    = "4"
,pages     = "1107-1135"
,year      = 2015
}


@article{emn16
,author    = "Eigel, M. and Merdon, C. and Neumann, J."
,title     = "An adaptive multilevel Monte Carlo method with stochastic
              bounds for quantities of interest with uncertain data"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    =  4
,number    = "1"
,pages     = "1219–1245"
,year      = "2016"
}

@article{ehm16
,author    = "Elfverson, D. and Hellman, F. and M{\aa}lqvist, A."
,title     = "A multilevel {M}onte {C}arlo method for computing
              failure probabilities"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    =  4
,number    = "1"
,pages     = "312-330"
,year      = "2016"
}

@phdthesis{emsermann00
,author    = "Emsermann, M."
,title     = "Variance reduction with quasi control variates"
,school    = "University of Colorado at Denver"
,type      = "{PhD} thesis"
,year      = "2000"
}

@article{es02
,author    = "Emsermann, M. and Simon, B."
,title     = "Improving simulation efficiency with quasi control variates"
,journal   = "Stochastic Models"
,volume    = "18"
,number    = "3"
,pages     = "425-448"
,year      = 2002
}

@article{fhmn16
,author    = "Fagerlund, F. and Hellman, F. and Malqvist, A. and Niemi, A."
,title     = "Multilevel {M}onte {C}arlo methods for computing failure
              probability of porous media flow systems"
,journal   = "Advances in Water Resources"
,volume    = "94"
,pages     = "498–509"
,year      = 2016
}

@article{fdki17
,author    = "Fairbanks, H. and Doostan, A. and Ketelsen, C. and Iaccarino, G."
,title     = "A low-rank control variate for multilevel {M}onte {C}arlo
              simulation of high-dimensional uncertain systems"
,journal   = "Journal of Computational Physics"
,volume    = "341"
,pages     = "121-139"
,year      = 2017
}

@article{fg16
,author    = "Fang, W. and Giles, M.B."
,title     = "Adaptive {E}uler-{M}aruyama method for {SDE}s with non-globally
              {L}ipschitz drift: {P}art {I}, finite time interval"
,journal   = "ArXiv preprint: 1609.08101"
,year      = 2016
}

@article{fg17
,author    = "Fang, W. and Giles, M.B."
,title     = "Adaptive {E}uler-{M}aruyama method for {SDE}s with non-globally
              {L}ipschitz drift: {P}art {II}, infinite time interval"
,journal   = "ArXiv preprint: 1703.06743"
,year      = 2017
}

@article{fg19
,author    = "Fang, W. and Giles, M.B."
,title     = "Multilevel {M}onte {C}arlo method for ergodic {SDE}s
              without contractivity"
,journal   = "Journal of Mathematical Analysis and Applications"
,volume    = "476"
,number    = "1"
,pages     = "149-176"
,year      = 2019
}

@article{fg20
,author    = "Fang, W. and Giles, M.B."
,title     = "Adaptive {E}uler-{M}aruyama method for {SDE}s with non-globally
              {L}ipschitz drift"
,journal   = "Annals of Applied Probability"
,volume    = "30"
,number    = "2"
,pages     = "526-560"
,year      = 2020
}

@article{fg21
,author    = "Fang, W. and Giles, M.B."
,title     = "Importance sampling for pathwise sensitivity of stochastic chaotic systems"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "9"
,number    = "3"
,pages     = "1217-1241"
,year      = 2021
}

@article{fwgjwat22
,author    = "Fang, W. and Wang, Z. and Giles, M.B. and Jackson, C.H.
              and Welton, N.J. and Andrieu, C. and Thom, H."
,title     = "Multilevel and quasi {M}onte {C}arlo methods for the calculation
              of the expected value of partial perfect information"
,journal   = "Medical Decision Making"
,volume    = "42"
,number    = "2"
,pages     = "168-181"
,year      = 2022
}

@article{fkss14
,author    = "Ferreiro-Castilla, A. and Kyprianou, A.E.
              and Scheichl, R. and Suryanarayana, G."
,title     = "Multi-level {M}onte-{C}arlo simulation for {L\'e}vy processes
              based on the {W}iener-{H}opf factorisation"
,journal   = "Stochastic Processes and their Applications"
,volume    = "124"
,number    = "2"
,pages     = "985-1010"
,year      = 2014
}

@article{fs15
,author    = "Ferreiro-Castilla, A. and van Schalk, K."
,title     = "Applying the {W}iener-{H}opf {M}onte {C}arlo simulation
              technique for{L\'e}vy processes to path functionals"
,journal   = "Journal of Applied Probability"
,volume    = "52"
,number    = "1"
,pages     = "129-148"
,year      = 2015
}

@article{frikha16
,author    = "Frikha, N."
,title     = "Applying the {W}iener-{H}opf {M}onte {C}arlo simulation
              technique for{L\'e}vy processes to path functionals"
,journal   = "Annals of Applied Probability"
,volume    = "26"
,number    = "2"
,pages     = "933-985"
,year      = 2016
}

@incollection{gss16
,author    = "Gantner, R.N. and Schillings, C. and Schwab, C."
,title     = "Binned multilevel {M}onte {C}arlo for {B}ayesian
              inverse problems with large data"
,series    = "Lecture Notes in Computational Science and Engineering"
,volume    = "104"
,publisher = "Springer"
,pages     = "511-519"
,year      = 2016
}

@incollection{gh13
,author    = "Gerstner, T. and Heinz, S."
,title     = "Dimension- and time-adaptive multilevel {M}onte {C}arlo methods"
,booktitle = "Sparse Grids and Applications"
,series    = "Lecture Notes in Computational Science and Engineering"
,volume    = "88"
,pages     = "107-120"
,publisher = "Springer"
,year      = "2013"
}

@incollection{gn13
,author    = "Gerstner, T. and Noll, M."
,title     = "Randomized multilevel quasi-{M}onte {C}arlo path simulation"
,booktitle = "Recent Developments in Computational Finance"
,publisher = "World Scientific"
,pages     = "349-372"
,year      = "2013"
}

@article{gb18
,author    = "Giles, M.B. and Bernal, F."
,title     = "Multilevel estimation of expected exit times and other functionals of stopped diffusions"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "6"
,number    = "4"
,pages     = "1454-1474"
,year      = "2018"
}

@article{gdr13
,author    = "Giles, M.B. and Debrabant, K. and R{\"o}{\ss}ler, A."
,title     = "Numerical analysis of multilevel {M}onte {C}arlo path
              simulation using the {M}ilstein discretisation"
,journal   = "ArXiv preprint: 1302.4676"
,year      = 2013
}

@article{gdr19
,author    = "Giles, M.B. and Debrabant, K. and R{\"o}{\ss}ler, A."
,title     = "Analysis of multilevel {M}onte {C}arlo path
              simulation using the {M}ilstein discretisation"
,journal   = "Discrete and Continuous Dynamical Systems - series B"
,volume    = "24"
,number    = "8"
,pages     = "3881-3903"
,year      = 2019
}

@article{gnr15
,author    = "Giles, M.B. and Nagapetyan, T. and Ritter, K."
,title     = "Multilevel {M}onte {C}arlo approximation of
              distribution functions and densities"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "3"
,number    = "1"
,pages     = "267-295"
,year      = "2015"
,url       = "http://www.dfg-spp1324.de/download/preprints/preprint157.pdf"
}

@article{giles08
,author    = "Giles, M.B."
,title     = "Multilevel {M}onte {C}arlo path simulation"
,journal   = "Operations Research"
,volume    = "56"
,number    = "3"
,pages     = "607-617"
,year      = "2008"
}

@incollection{giles08b
,author    = "Giles, M.B."
,title     = "Improved multilevel {M}onte {C}arlo convergence
              using the {M}ilstein scheme"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2006"
,editor    = "Keller, A. and Heinrich, S. and Niederreiter, H."
,pages     = "343-358"
,year      = "2008"
}

@incollection{giles09
,author    = "Giles, M.B."
,title     = "Multilevel {M}onte {C}arlo for Basket Options"
,booktitle = "Proceedings of the 2009 Winter Simulation Conference"
,publisher = "IEEE"
,editor    = "Rossetti, M.D. and Hill, R.R. and Johansson, B. and Dunkin, A. and Ingalls, R.G."
,pages     = "1283-1290"
,year      = "2009"
}

@article{ghm09
,author    = "Giles, M.B. and Higham, D.J. and Mao, X."
,title     = "Analysing multilevel {M}onte {C}arlo for options with
              non-globally {L}ipschitz payoff"
,journal   = "Finance and Stochastics"
,volume    = "13"
,number    = "3"
,pages     = "403-413"
,year      = "2009"
}

@incollection{gks18
,author    = "Giles, M.B. and Kuo, F.Y. and Sloan, I.H."
,title     = "Combining sparse grids, multilevel {MC} and {QMC}
              for elliptic {PDE}s with random coefficients"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2016"
,editor    = "Glynn, P.W. and Owen, A."
,year      = "2018"
}

@article{gmsvz20
,author    = "Giles, M.B. and Majka, M.B. and Szpruch, L. and
              Vollmer, S.J. and Zygalakis, K.C."
,title     = "Multi-level {M}onte {C}arlo methods for the approximation
         of invariant measures of stochastic differential equations"
,journal   = "Statistics and Computing"
,volume    = "30"
,number    = "3"
,pages     = "507-524"
,year      = "2020"
}

@incollection{gw09
,author    = "Giles, M.B. and Waterhouse, B.J."
,title     = "Multilevel quasi-{M}onte {C}arlo path simulation"
,booktitle = "Advanced Financial Modelling"
,series    = "Radon Series on Computational and Applied Mathematics"
,publisher = "De Gruyter"
,pages     = "165-181"
,year      = "2009"
}

@article{gr12
,author    = "Giles, M.B. and Reisinger, C."
,title     = "Stochastic finite differences and multilevel {M}onte {C}arlo
              for a class of {SPDEs} in finance"
,journal   = "SIAM Journal of Financial Mathematics"
,volume    = "3"
,number    = "1"
,pages     = "572-592"
,year      = "2012"
}

@article{gs14
,author    = "Giles, M.B. and Szpruch, L."
,title     = "Antithetic multilevel {M}onte {C}arlo estimation for
              multi-dimensional {SDE}s without {L\'e}vy area simulation"
,journal   = "Annals of Applied Probability"
,volume    = "24"
,number    = "4"
,pages     = "1585-1620"
,year      = "2014"
}

@incollection{gs13
,author    = "Giles, M.B. and Szpruch, L."
,title     = "Multilevel {M}onte {C}arlo methods for applications in finance"
,publisher = "World Scientific"
,booktitle = "Recent Developments in Computational Finance"
,pages     = "3-48"
,year      = "2013"
}

@incollection{gs13b
,author    = "Giles, M.B. and Szpruch, L."
,title     = "Antithetic multilevel {M}onte {C}arlo estimation for
              multidimensional {SDE}s"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2012"
,editor    = "Dick, J. and Kuo, F.Y. and Peters, G.W. and Sloan, I.H."
,pages     = "367-384"
,year      = "2013"
}

@incollection{giles13
,author    = "Giles, M.B."
,title     = "Multilevel {M}onte {C}arlo methods"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2012"
,editor    = "Dick, J. and Kuo, F.Y. and Peters, G.W. and Sloan, I.H."
,pages     = "83-103"
,year      = "2013"
}

@article{giles15
,author    = "Giles, M.B."
,title     = "Multilevel {M}onte {C}arlo methods"
,publisher = "Cambridge University Press"
,journal   = "Acta Numerica"
,volume    = "24"
,pages     = "259-328"
,year      = "2015"
}

@incollection{glw16
,author    = "Giles, M.B. and Lester, C. and Whittle, J."
,title     = "Non-nested adaptive timesteps in multilevel {M}onte {C}arlo
              computations"
,pages     = "303-314"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2014"
,editor    = "Cools, R. and Nuyens, D."
,year      = "2016"
}

@article{gg19
,author    = "Giles, M.B. and Goda, T."
,title     = "Decision-making under uncertainty: using {MLMC}
              for efficient estimation of {EVPPI}"
,journal   = "Statistics and Computing"
,volume    = "29"
,number    = "4"
,pages     = "739-751"
,year      = 2019
}

@article{gg17
,author    = "Giles, M.B. and Goda, T."
,title     = "Decision-making under uncertainty: using {MLMC}
              for efficient estimation of {EVPPI}"
,journal   = "ArXiv preprint: 1708.05531"
,year      = 2017
}

@article{gr17
,author    = "Giles, M.B. and Ramanan, K."
,title     = "{MLMC} with adaptive timestepping for reflected
              {B}rownian diffusions"
,journal   = "In preparation"
,year      = 2017
}

@article{gx17
,author    = "Giles, M.B. and Xia, Y."
,title     = "Multilevel {M}onte {C}arlo for exponential {L\'e}vy models"
,journal   = "Finance and Stochastic"
,volume    = "21"
,number    = "4"
,pages     = "995-1026"
,year      = 2017
}

@article{gh19
,author    = "Giles, M.B. and Haji-Ali, A.-L."
,title     = "Multilevel nested simulation for efficient risk estimation"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "7"
,number    = "2"
,pages     = "497-525"
,year      = "2019"
}

@article{gh22
,author    = "Giles, M.B. and Haji-Ali, A.-L."
,title     = "Sub-sampling and other considerations for efficient
              risk estimation in large portfolios"
,journal   = "Journal of Computational Finance"
,volume    = "26"
,number    = "1"
,year      = "2022"
}

@article{gh24
,author    = "Giles, M.B. and Haji-Ali, A.-L."
,title     = "Multilevel path branching for digital options"
,journal   = "Annals of Applied Probability"
,volume    = "34"
,number    = "5"
,pages     = "4836-4862"
,year      = "2024"
}

@article{ghs25
,author    = "Giles, M.B. and Haji-Ali, A.-L. and Spence, J."
,title     = "Efficient risk estimation for the credit valuation adjustment"
,journal   = "Journal of Computational Finance"
,year      = "2025"
}

@incollection{giles18
,author    = "Giles, M.B."
,title     = "{MLMC} for nested expectations"
,booktitle = "Contemporary Computational Mathematics - A Celebration of
              the 80th Birthday of Ian Sloan"
,publisher = "Springer"
,year      = "2018"
}

@article{ghmr19
,author    = "Giles, M.B. and Hefter, M. and Mayer, L. and Ritter, K."
,title     = "Random bit quadrature and approximation of distributions
              on {H}ilbert spaces"
,journal   = "Foundations of Computational Mathematics"
,volume    = "19"
,number    = "1"
,pages     = "205-238"
,year      = "2019"
}

@article{ghmr19b
,author    = "Giles, M.B. and Hefter, M. and Mayer, L. and Ritter, K."
,title     = "Random bit multilevel algorithms for stochastic
              differential equations"
,journal   = "Journal of Complexity"
,volume    = "54"
,pages     = "10139519"
,year      = "2019"
}

@incollection{ghmr20
,author    = "Giles, M.B. and Hefter, M. and Mayer, L. and Ritter, K."
,title     = "An adaptive random bit multilevel algorithm for {SDE}s"
,booktitle = "Multivariate Algorithms and Information-Based Complexity"
,publisher = "de Gruyter"
,year      = "2020"
}

@article{gs22
,author    = "Giles, M.B. and Sheridan-Methven, O."
,title     = "Analysis of nested multilevel {M}onte {C}arlo using
              approximate {N}ormal random variables"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "10"
,number    = "1"
,pages     = "200-226"
,year      = "2022"
}

@article{gs23
,author    = "Giles, M.B. and Sheridan-Methven, O."
,title     = "Approximating inverse cumulative distribution functions
              to produce approximate random variables"
,journal   = "ACM Transactions on Mathematical Software"
,volume    = "49"
,number    = "3"
,pages     = "1-29"
,year      = "2023"
}

@booklet{giles_MLMC_code
,author    = "Giles, M.B."
,title     = "MATLAB code for multilevel {M}onte {C}arlo computations"
,howpublished = "{\tt http://people.maths.ox.ac.uk/gilesm/acta/}"
,year      = "2014"
}

@booklet{MLMC_community
,author    = "Giles, M.B."
,title     = "Multilevel {M}onte {C}arlo research community and papers"
,howpublished = "{\tt http://people.maths.ox.ac.uk/gilesm/mlmc\_community/}"
,year      = "2015"
}

@article{glp17
,author    = "Giorgi, D. and Lemaire, V. and Pag{\`e}s, G."
,title     = "Limit theorems for weighted and regular multilevel estimators"
,journal   = "Monte Carlo Methods and Applications"
,volume    = 31
,number    = 1
,pages     = "43-70"
,year      = "2017"
}

@article{gkss13
,author    = "Gittelson, C.J. and Konno, J. and Schwab, C. and Stenberg, R."
,title     = "The multi-level {M}onte {C}arlo finite element method
              for a stochastic {B}rinkman problem"
,journal   = "Numerische Mathematik"
,volume    = 125
,pages     = "347-386"
,year      = "2013"
}

@article{gr14
,author    = "Glynn, P.W. and Rhee, C.-H."
,title     = "Exact estimation for {M}arkov chain equilibrium expectations"
,journal   = "Journal of Applied Probability"
,volume    = 51
,pages     = "377-389"
,year      = "2014"
}

@incollection{glynn16
,author    = "Glynn, P.W."
,title     = "Exact simulation vs.~exact estimation"
,booktitle = "Proceedings of the 2016 Winter Simulation Conference"
,publisher = "IEEE"
,year      = "2016"
}

@article{gnewuch12
,author    = "Gnewuch, M."
,title     = "Infinite-dimensional integration on weighted {H}ilbert spaces"
,journal   = "Mathematics of Computation"
,volume    = 81
,number    = 280
,pages     = "2175-2205"
,year      = 2012
}

@article{gnewuch13
,author    = "Gnewuch, M."
,title     = "Lower error bounds for randomized multilevel
              and changing dimension algorithms"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2012"
,editor    = "Dick, J. and Kuo, F.Y. and Peters, G.W. and Sloan, I.H."
,pages     = "399-415"
,year      = "2013"
}

@article{goda16
,author    = "Goda, T."
,title     = "Unbiased {M}onte {C}arlo estimation for the
              expected value of partial perfect information"
,journal   = "ArXiv preprint: 1604.01120"
,year      = 2016
}

@phdthesis{gou16
,author    = "Gou, W."
,title     = "Estimating {V}alue-at-{R}isk using multilevel
              {M}onte {C}arlo {M}aximum {E}ntropy method"
,school    = "University of Oxford"
,type      = "{MSc} thesis"
,year      = "2016"
,url       = "http://people.maths.ox.ac.uk/~gilesm/files/WenhuiGou.pdf"
}

@article{gsu15
,author    = "Graham, I.G. and Scheichl, R. and Ullmann, E."
,title     = "Mixed finite element analysis of lognormal diffusion
              and multilevel {M}onte {C}arlo methods"
,journal   = "Stochastic Partial Differential Equations:
              Analysis and Computations"
,pages     = "1-35"
,year      = "2015"
}

@report{graubner08_old
,author    = "Graubner, S."
,title     = "Multi-level {M}onte {C}arlo {M}ethoden f{\"u}r stochastische
              partielle {D}ifferentialgleichungen"
,institution = "TU Darmstadt"
,type      = "Diplomarbeit"
,year      = 2008
}

@phdthesis{graubner08
,author    = "Graubner, S."
,title     = "Multi-level {M}onte {C}arlo {M}ethoden f{\"u}r stochastische
              partielle {D}ifferentialgleichungen"
,school    = "TU Darmstadt"
,type      = "Diplomarbeit"
,year      = 2008
}

@article{gcr16
,author    = "Gregory, A. and Cotter, C.J. and Reich, S."
,title     = "Multilevel ensemble transform particle filtering"
,journal   = "SIAM Journal on Scientific Computing"
,volume    = "38"
,number    = "3"
,pages     = "1317–1338"
,year      = "2016"
}

@article{gc17
,author    = "Gregory, A. and Cotter, C.J."
,title     = "On the calibration of multilevel {M}onte {C}arlo ensemble forecasts"
,journal   = "Quarterly Journal of the Royal Meteorological Society"
,volume    = "143"
,number    = "705"
,pages     = "1929-1935"
,year      = "2017"
}

@phdthesis{gruhlke14
,author    = "Gruhlke, D."
,title     = "Convergence of {M}ultilevel {MCMC} methods on path spaces"
,school    = "University of Bonn"
,type      = "{PhD} thesis"
,year      = "2014"
,url       = "http://hss.ulb.uni-bonn.de/2014/3667/3667.pdf"}

@article{gt17
,author    = "Guha, N. and Tan, X."
,title     = "Multilevel approximate Bayesian approaches for flows in
              highly heterogeneous porous media and their applications"
,journal   = "Journal of Computational and Applied Mathematics"
,volume    = "317"
,pages     = "700-717"
,year      = 2017
}

@phdthesis{hajiali12
,author    = "Haji-Ali, A.-L."
,title     = "Pedestrian flow in the mean-field limit"
,school    = "KAUST"
,type      = "{MSc} thesis"
,year      = "2012"
,url       = "http://stochastic_numerics.kaust.edu.sa/Documents/publications/AbdulLateef%20Haji%20Ali%20_Thesis.pdf"
}

@article{hnst16
,author    = "Haji-Ali, A.-L. and Nobile, F. and von Schwerin, E. and Tempone, R."
,title     = "Optimization of mesh hierarchies in multilevel {M}onte {C}arlo samplers"
,journal   = "Stochastics and PDEs: Analysis and Computations"
,volume    = "4"
,number    = "1"
,pages     = "76–112"
,year      = "2016"
}

@article{hnt16
,author    = "Haji-Ali, A.-L. and Nobile, F. and Tempone, R."
,title     = "Multi {I}ndex {M}onte {C}arlo: when sparsity meets sampling"
,journal   = "Numerische Mathematik"
,volume    = "132"
,number    = "4"
,pages     = "767-806"
,year      = "2016"
}

@article{ht18
,author    = "Haji-Ali, A.-L. and Tempone, R."
,title     = "Multilevel and multi-index {M}onte {C}arlo methods for
              {M}c{K}ean-{V}lasov equations"
,journal   = "Statistics and Computing"
,volume    = "28"
,pages     = "923-935"
,year      = "2018"
}

@article{hst22
,author    = "Haji-Ali, A.-L. and Spence, J. and Teckentrup, A."
,title     = "Adaptive multilevel {M}onte {C}arlo for probabilities"
,journal   = "SIAM Journal on Numerical Analysis"
,volume    = "60"
,number    = "4"
,pages     = "2125-2149"
,year      = "2022"
}

@article{hs25
,author    = "Haji-Ali, A.-L. and Stein, A."
,title     = "An antithetic multilevel {M}onte {C}arlo-{M}ilstein scheme for
              stochastic partial differential equations with non-commutative noise"
,journal   = "ESAIM Mathematical Modelling and Numerical Analysis"
,volume    = "59"
,number    = "3"
,pages     = "1437-1470"
,year      = "2025"
}

@incollection{hps13
,author    = "Harbrecht, H. and Peters, M. and Siebenmorgen, M."
,title     = "On multilevel quadrature for elliptic stochastic
              partial differential equations"
,booktitle = "Sparse Grids and Applications"
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,volume    = "88"
,pages     = "161-179"
,publisher = "Springer"
,year      = "2013"
}

@article{hps16
,author    = "Harbrecht, H. and Peters, M. and Siebenmorgen, M."
,title     = "Multilevel accelerated quadrature for {PDE}s with
              log-{N}ormally distributed diffusion coefficient"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "4"
,number    = "1"
,pages     = "520–551"
,year      = "2016"
}

@article{heinrich98
,author    = "Heinrich, S."
,title     = "{M}onte {C}arlo complexity of global solution
              of integral equations"
,journal   = "Journal of Complexity"
,volume    = 14
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,year      = 1998
}

@article{hs99
,author    = "Heinrich, S. and Sindambiwe, E."
,title     = "{M}onte {C}arlo complexity of parametric integration"
,journal   = "Journal of Complexity"
,volume    = 15
,number    = 3
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,year      = 1999
}

@incollection{heinrich00
,author    = "Heinrich, S."
,title     = "The multilevel method of dependent tests"
,booktitle = "Advances in Stochastic Simulation Methods"
,publisher = "Springer"
,editor    = "Balakrishnan, N. and Melas, V.B. and Ermakov, S."
,pages     = "47-61"
,year      = 2000
}

@incollection{heinrich01
,author    = "Heinrich, S."
,title     = "Multilevel {M}onte {C}arlo Methods"
,series    = "Lecture Notes in Computer Science"
,publisher = "Springer"
,year      = "2001"
,volume    = "2179"
,pages     = "58-67"
,booktitle = "Multigrid Methods"
}

@article{heinrich06
,author    = "Heinrich, S."
,title     = "{M}onte {C}arlo approximation of weakly singular
              integral operators"
,journal   = "Journal of Complexity"
,volume    = 22
,number    = 2
,pages     = "192-219"
,year      = 2006
}

@article{hmnr10
,author    = "Hickernell, F.J. and M{\"u}ller-Gronbach, T. and
              Niu, B. and Ritter, K."
,title     = "Multi-level Monte Carlo algorithms for infinite-dimensional
              integration on $\mathbb{R}^{N}$"
,journal   = "Journal of Complexity"
,volume    = 26
,number    = 3
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,year      = 2010
}

@article{higham11
,author    = "Higham, D.J."
,title     = "Stochastic ordinary differential equations in applied and
              computational mathematics"
,journal   = "IMA Journal of Applied Mathematics"
,volume    = 76
,number    = 3
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,year      = 2011
}

@article{higham15
,author    = "Higham, D.J."
,title     = "An introduction to multilevel {M}onte {C}arlo for option valuation"
,journal   = "International Journal of Computer Mathematics"
,volume    = 92
,number    = 12
,pages     = "2347-2360"
,year      = 2015
}

@article{hmrsy13
,author    = "Higham, D.J. and Mao, X. and  Roj, M. and Song, Q. and Yin, G."
,title     = "Mean exit times and the multi-level {M}onte {C}arlo method"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "1"
,number    = "1"
,pages     = "2-18"
,year      = "2013"
}

@article{hggt20
,author    = "Hironaka, T. and Giles, M.B. and Goda, T. and Thom, H."
,title     = "Multilevel {M}onte {C}arlo estimation of the expected value
              of sample information"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "8"
,number    = "3"
,pages     = "1236-1259"
,year      = "2020"
}

@article{hss13
,author    = "Hoang, V.H. and Schwab, C. and Stuart, A.M."
,title     = "Complexity analysis of accelerated {MCMC} methods
              for {B}ayesian inversion"
,journal   = "Inverse Problems"
,url       = "http://dx.doi.org/10.1088/0266-5611/29/8/085010"
,volume    = 29
,number    = 8
,year      = 2013
}

@incollection{hsst12
,author    = "Hoel, H. and von Schwerin, E. and Szepessy, A. and Tempone, R."
,title     = "Adaptive multilevel {M}onte {C}arlo simulation"
,booktitle = "Numerical Analysis of Multiscale Computations"
,publisher = "Springer"
,series    = "Lecture Notes in Computational Science and Engineering"
,editor    = "Engquist, B. and Runborg, O. and Tsai, Y.-H.R."
,number    = "82"
,pages     = "217-234"
,year      = "2012"
}

@article{hsst14
,author    = "Hoel, H. and von Schwerin, E. and Szepessy, A. and Tempone, R."
,title     = "Implementation and analysis of an adaptive multilevel
              {M}onte {C}arlo algorithm"
,journal   = "Monte Carlo Methods and Applications"
,volume    = "20"
,number    = "1"
,pages     = "1-41"
,year      = "2014"
}

@article{hlt16
,author    = "Hoel, H. and Law, K.J.H. and Tempone, R."
,title     = "Multilevel ensemble Kalman filtering"
,journal   = "SIAM Journal of Numerical Analysis"
,volume    = "54"
,number    = "3"
,pages     = "1813-1839"
,year      = "2016"
}

@article{hz17
,author    = "Huda, A.S.N. and Zivanovic, R."
,title     = "Improving distribution system reliability calculation
              efficiency using multilevel {M}onte {C}arlo method"
,journal   = "Int.~Trans.~Electrical Energy Systems"
,volume    = "27"
,number    = "7"
,year      = "2017"
}

@article{ibt16
,author    = "Icardi, M. and Boccardo, G. and Tempone, R."
,title     = "On the predictivity of pore-scale simulations: estimating
              uncertainties with multilevel {M}onte {C}arlo"
,journal   = "Advances in Water Resources"
,volume    = "95"
,pages     = "6–60"
,year      = "2016"
}

@article{hjk13
,author    = "Hutzenthaler, M. and Jentzen, A. and Kloeden, P.E."
,title     = "Divergence of the multilevel {M}onte {C}arlo method"
,journal   = "Annals of Applied Probability"
,volume    = "23"
,number    = "5"
,pages     = "1913-1966"
,year      = "2013"
}

@incollection{inr13
,author    = "Iliev, O. and Nagapetyan, T. and Ritter, K."
,title     = "Monte {C}arlo simulation of asymmetric flow field
              flow fractionation"
,publisher = "de Gruyter"
,booktitle = "Monte Carlo Methods and Applications: Proceedings
              of the 8th IMACS Seminar on Monte Carlo Methods"
,pages     = "115-123"
,year      = "2013"
}

@article{kmssgt18
,author    = "Katsiolides, G. and M{\"u}ller, E.H. and Scheichl, R. and
              Shardlow, T. and Giles, M.B. and Thomson, D.J."
,title     = "Multilevel {M}onte {C}arlo and improved timestepping
              methods in atmospheric dispersion modelling"
,journal   = "Journal of Computational Physics"
,volume    = "354"
,number    = "1"
,pages     = "320-343"
,year      = "2018"
}

@article{kebaier05
,author    = "Kebaier, A."
,title     = "Statistical {R}omberg extrapolation: a new variance
              reduction method and applications to options pricing"
,journal   = "Annals of Applied Probability"
,volume    = 14
,number    = 4
,pages     = "2681-2705"
,year      = 2005
}

@article{kk08
,author    = "Kebaier, A. and Kohatsu-Higa, A."
,title     = "An optimal control variance reduction method for
              density estimation"
,journal   = "Stochastic Processes and their Applications"
,volume    = 118
,number    = 2
,pages     = "2143-2180"
,year      = 2008
}

@article{keller01
,author  =  "Keller, A."
,title   =  "Hierarchical {M}onte {C}arlo Image Synthesis"
,journal =  "Mathematics and Computers in Simulation"
,volume  =  55
,number  =  "1-3"
,pages   =  "79-92"
,year    =  2001
}

@article{kth18
,author    = "Khodadadian, A. and Taghizadeh, L. and Heitzinger, C."
,title     = "Optimal multilevel randomized quasi-{M}onte-{C}arlo method
              for the stochastic drift–diffusion-{P}oisson system"
,journal   = "Computer Methods in Applied Mechanics and Engineering"
,volume    = "329"
,pages     = "480-497"
,year      =
2018
}

@article{kpadh19
,author    = "Khodadadian, A. and Parvizi, M. and Abbaszadeh, M. 
              and Dehghan, M. and Heitzinger, C."
,title     = "A multilevel {M}onte {C}arlo finite element method for
              the stochastic {C}ahn–{H}illiard–{C}ook equation"
,journal   = "Computational Mechanics"
,volume    = "64"
,pages     = "937-949"
,year      = 2019
}

@article{knp11
,author    = "Kloeden, P. and Neuenkirch, A. and Pavani, R."
,title     = "Multilevel {M}onte {C}arlo for stochastic differential
              equations with additive fractional noise"
,journal   = "Annals of Operations Research"
,volume    = "189"
,number    = "1"
,pages     = "255-276"
,year      = 2011
}

@article{ksw14
,author  =  "Kornhuber, R. and Schwab, C. and Wolf, M.-W."
,title   =  "Multilevel {M}onte {C}arlo finite element methods for stochastic
             elliptic variational inequalities"
,journal =  "SIAM Journal on Numerical Analysis"
,volume  =  52
,number  =  "3"
,pages   =  "1243-1268"
,year    =  2014
}

@phdthesis{kronsbein12
,author    = "Kronsbein, C."
,title     = "Numerical Approximation for SDE"
,school    = "Technischen Universit{\"a}t Kaiserslautern"
,type      = "{PhD} thesis"
,year      = "2012"
}

@article{kn18
,author    = "Krumscheid, S. and Nobile, F."
,title     = "Multilevel {M}onte {C}arlo approximation of functions"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "6"
,number    = "3"
,pages     = "1256-1293"
,year      = "2018"
}

@article{kod17
,author    = "Kumar, P. and Oosterlee, C.W. and Dwight, R.P."
,title     = "A multigrid multilevel {M}onte {C}arlo method using high-order
              finite-volume scheme for lognormal diffusion problems"
,journal   = "International Journal for Uncertainty Quantification"
,year      = "2017"
}

@article{kn16
,author    = "Kuo, F.Y. and Nuyens, D."
,title     = "Application of {Q}uasi-{M}onte {C}arlo methods to elliptic
              {PDE}s with random diffusion coefficients: a survey of
               analysis and implementation"
,journal   = "Foundations of Computational Mathematics"
,volume    =  16
,number    = "6"
,pages     = "1631-1696"
,year      = "2016"
}

@article{ksssu17
,author    = "Kuo, F.Y. and Scheichl, R. and Schwab, C.
              and Sloan, I.H. and Ullmann, E."
,title     = "Multilevel quasi-{M}onte {C}arlo methods for
              lognormal diffusion problems"
,journal   = "Mathematics of Computation"
,year      = "online, March 2017"
}

@article{kss15
,author    = "Kuo, F.Y. and Schwab, C. and Sloan, I.H."
,title     = "Multi-level quasi-{M}onte {C}arlo finite element
              methods for a class of elliptic partial
              differential equations with random coefficients"
,journal   = "Foundations of Computational Mathematics"
,volume    =  15
,number    = "2"
,pages     = "411-449"
,year      = "2015"
}

@article{lp18
,author    = "Lang, A. and Petersson, A."
,title     = "Monte {C}arlo versus multilevel {M}onte {C}arlo in
              weak error simulations of {SPDE} approximations"
,journal   = "Mathematics and Computers in Simulation"
,volume    =  143
,pages     = "99-113"
,year      = "2018"
}

@article{lp13
,author    = "Lemaire, V. and Pag{\`e}s, G."
,title     = "Multilevel {R}ichardson-{R}omberg extrapolation"
,journal   = "ArXiv preprint: 1401.1177"
,year      = "2013"
}

@article{lp17
,author    = "Lemaire, V. and Pag{\`e}s, G."
,title     = "Multilevel {R}ichardson-{R}omberg extrapolation"
,journal   = "Bernoulli"
,volume    =  "23"
,number    = "4A"
,pages     = "2643-2692"
,year      = "2017"
}

@article{lygb15
,author    = "Lester, C. and Yates, C. and Giles, M.B. and Baker, R."
,title     = "An adaptive multi-level simulation algorithm
              for stochastic biological systems"
,journal   = "Journal of Chemical Physics"
,volume    = 142
,number    = 2
,month     = "Jan"
,year      = "2015"
}

@article{lbgy16
,author    = "Lester, C. and Baker, R. and Giles, M.B. and Yates, C."
,title     = "Extending the multi-level method for the simulation
              of stochastic biological systems"
,journal   = "Bulletin of Mathematical Biology"
,volume    = 78
,number    = 8
,pages     = "1640-1677"
,year      = "2016"
}

@article{lbgy14
,author    = "Lester, C. and Baker, R. and Giles, M.B. and Yates, C."
,title     = "A guide to efficient discrete-state multi-level
              simulation of stochastic biological systems"
,journal   = "ArXiv preprint: 1412.4069"
,year      = "2014"
}

@phdthesis{li07
,author    = "Li, Q."
,title     = "N-dimension numerical solution of stochastic
              differential equations"
,school    = "University of Edinburgh"
,type      = "{PhD} thesis"
,year      = "2007"
}

@incollection{lll16
,author    = "Lindsey, B. and Leslie, M. and Luk, W."
,title     = "A domain specific language for accelerated multilevel
              {M}onte {C}arlo simulations"
,booktitle = "Proceedings of the 27th International Conference on
              Application-specific Systems, Architectures and Processors"
,publisher = "IEEE"
,year      = "2016"
}

@article{mba16
,author    = "Mancini, S. and Bernal, F. and Acebron, J.A."
,title     = "An efficient algorithm for accelerating {M}onte {C}arlo
              approximations of the solution to boundary value problems"
,journal   = "Journal of Scientific Computing"
,volume    = 66
,number    = 2
,pages     = "577-597"
,year      = 2016
}

@article{marxen10
,author    = "Marxen, H."
,title     = "The multilevel {M}onte {C}arlo method used on a
              {L\'e}vy driven {SDE}"
,journal   = "Monte Carlo Methods and Applications"
,volume    = 16
,number    = 2
,pages     = "167-190"
,year      = 2010
}

@article{mpv17
,author    = "Mbaye, C. and Pag{\`e}s, G. and Vrins, F"
,title     = "An antithetic approach of multilevel {R}ichardson-{R}omberg
              extrapolation estimator for multidimensional {SDE}s"
,journal   = "Numerical Analysis and its Applications"
,year      = 2017
}

@article{mcleish11
,author    = "McLeish, D."
,title     = "A general method for debiasing a {M}onte {C}arlo estimator"
,journal   = "Monte Carlo Methods and Applications"
,volume    = 17
,number    = 4
,pages     = "301-315"
,year      = 2011
}

@article{mss12
,author    = "Mishra, S. and Schwab, C. and Sukys, J."
,title     = "Multi-level {M}onte {C}arlo finite volume
              methods for nonlinear systems of conservation
              laws in multi-dimensions"
,journal   = "Journal of Computational Physics"
,volume    = 231
,number    = 8
,pages     = "3365-3388"
,year      = 2012
}

@article{mss12b
,author    = "Mishra, S. and Schwab, C. and Sukys, J."
,title     = "Multi-level {M}onte {C}arlo finite volume
              methods for shallow water equations with
              uncertain topography in multi-dimensions"
,journal   = "SIAM Journal on Scientific Computing"
,volume    = 34
,number    = 6
,pages     = "761-784"
,year      = 2012
}

@article{mss16
,author    = "Mishra, S. and Schwab, C. and Sukys, J."
,title     = "Multi-level {M}onte {C}arlo finite volume methods
              for uncertainty quantification of acoustic wave
              propagation in random heterogeneous layered medium"
,journal   = "Journal of Computational Physics"
,volume    = 312
,number    = 5
,pages     = "192-217"
,year      = 2016
}

@incollection{mmnkiob15
,author    = "Mohring, J, and Milk, R. and Ngo, A. and Klein, O.
              and Iliev, O. and Ohlberger, M. and Bastian, P."
,title     = "Uncertainty quantification for porous media flow
              using multilevel {M}onte {C}arlo"
,booktitle = "Large-Scale Scientific Computing"
,series    = "Lecture Notes in Computer Science"
,publisher = "Springer"
,volume    = "9374"
,pages     = "145-152"
,year      = 2015
}

@article{mtv14
,author    = "Moraes, A. and Tempone, R. and Vilanova, P."
,title     = "Multilevel hybrid {C}hernoff tau-leap"
,journal   = "SIAM Journal on Multiscale Modeling \& Simulation"
,volume    = 12
,number    = 2
,pages     = "581-615"
,year      = "2014"
}

@article{mtv16
,author    = "Moraes, A. and Tempone, R. and Vilanova, P."
,title     = "A multilevel adaptive reaction-splitting simulation
              method for stochastic reaction networks"
,journal   = "SIAM Journal on Scientific Computing"
,volume    = 38
,number    = 4
,pages     = "A2091-A2117"
,year      = "2016"
}

@article{mjm13
,author    = "M{\"u}ller, F. and Jenny, P. and Meyer, D.W."
,title     = "Multilevel {M}onte {C}arlo for two phase flow
              and {B}uckley-{L}everett transport in
              random heterogeneous porous media"
,journal   = "Journal of Computational Physics"
,volume    = "250"
,pages     = "685-702"
,year      = "2013"
}

@article{mjm16
,author    = "M{\"u}ller, F. and Jenny, P. and Meyer, D.W."
,title     = "Parallel multilevel {M}onte {C}arlo for two phase flow
              and transport in random heterogeneous porous media With
              sampling-error and discretization-error balancing"
,journal   = "SPE Journal"
,volume    = "21"
,number    = "6"
,pages     = "2027-2037"
,year      = "2016"
}

@article{mmj14
,author    = "M{\"u}ller, F. and Meyer, D.W. and Jenny, P."
,title     = "Solver-based vs. grid-based multilevel {M}onte {C}arlo
              for two phase flow and transport in random heterogeneous
              porous media"
,journal   = "Journal of Computational Physics"
,volume    = "268"
,pages     = "39-50"
,year      = "2014"
}

@incollection{mr08
,author    = "M{\"u}ller-Gronbach, T. and Ritter, K."
,title     = "Minimal errors for strong and weak approximation of stochastic
              differential equations"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2006"
,editor    = "Keller, A. and Heinrich, S. and Niederreiter, H."
,pages     = "53-82"
,year      = "2008"
}

@incollection{mr09
,author    = "M{\"u}ller-Gronbach, T. and Ritter, K."
,title     = "Variable subspace sampling and multi-level algorithms"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2008"
,editor    = "L'Ecuyer, P. and Owen, A."
,pages     = "131-156"
,year      = "2009"
}

@article{mss15
,author    = "M{\"u}ller, E.H. and Scheichl, R. and Shardlow, T."
,title     = "Improving multilevel {M}onte {C}arlo for stochastic differential
              equations with application to the {L}angevin equation"
,journal   = "Royal Society Proceedings A"
,volume    = 471
,number    = "2176"
,year      = 2015
}

@article{ns14
,author    = "Neuenkirch, A. and Szpruch, L."
,title     = "First order strong approximations of scalar
              {SDE}s defined in a domain"
,journal   = "Numerische Mathematik"
,volume    = "128"
,number    = "1"
,pages     = "103-136"
,year      = 2014
}

@article{nt18
,author    = "Neum{\"u}ller, M. and Thalhammer, A."
,title     = "A fully parallelizable space-time multilevel {M}onte {C}arlo
              method for stochastic differential equations with additive noise"
,journal   = "SIAM Journal on Scientific Computing"
,volume    = "40"
,number    = "3"
,pages     = "C388-400"
,year      = 2018
}

@phdthesis{niu11
,author    = "Niu, B."
,title     = "Monte {C}arlo simulation of infinite-dimensional integrals"
,school    = "Illinois Institute of Technology"
,type      = "{PhD} thesis"
,year      = "2011"
}

@article{nhmr10
,author    = "Niu, B. and Hickernell, F.J. and 
              M{\"u}ller-Gronbach, T. and Ritter, K."
,title     = "Deterministic multi-level algorithms for infinite-dimensional
              integration on $\mathbb{R}^{N}$"
,journal   = "Journal of Complexity"
,volume    = 27
,number    = "3-4"
,pages     = "331-351"
,year      = 2010
}

@article{nt15
,author    = "Nobile, F. and Tesei, F."
,title     = "A multilevel {M}onte {C}arlo method with control variate
              for elliptic {PDE}s with log-normal coefficients"
,journal   = "Stochastic Partial Differential Equations: Analysis and Computations"
,volume    = "3"
,number    = "3"
,pages     = "398-444"
,year      = 2015
}

@incollection{ohrbswk15
,author    = "Omland, S. and Hefter, M. and Ritter, K. and Brugger, C.
              and de Schryver, C. and Wehn, N. and Kostiuk, A."
,title     = "Exploiting mixed-precision arithmetic in a multilevel
              {M}onte {C}arlo approach on {FPGA}s"
,booktitle = "FPGA Based Accelerators for Financial Applications"
,publisher = "Springer"
,year      = "2015"
}

@article{pas15
,author    = "Pauli, S. and Arbenz, P. and Schwab, C."
,title     = "Intrinsic fault tolerance of multilevel {M}onte {C}arlo methods"
,journal   = "Journal of Parallel and Distributed Computing"
,volume    = "84"
,pages     = "24-36"
,year      = 2015
}

@article{pa15
,author    = "Pauli, S. and Arbenz, P."
,title     = "Determining optimal multilevel {M}onte {C}arlo parameters
              with application to fault tolerance"
,journal   = "Computers & Mathematics with Applications"
,volume    = "70"
,number    = "11"
,pages     = "2638-2651"
,year      = 2015
}

@article{pgaa15
,author    = "Pauli, S. and Gantner, R.N. and Arbenz, P. and Adelmann, A."
,title     = "Multilevel {M}onte {C}arlo for the {F}eynman–{K}ac
              formula for the {L}aplace equation"
,journal   = "BIT Numerical Mathematics"
,volume    = "55"
,number    = "4"
,pages     = "1125-1143"
,year      = 2015
}

@incollection{petersson2020
,author    = "Petersson, A."
,title     = "Rapid Covariance-Based Sampling of Linear {SPDE}
              Approximations in the Multilevel Monte Carlo Method"
,booktitle = "Proceedings of MCQMC 2018"
,publisher = "Springer"
,year      = "2020"
}

@phdthesis{primozic11
,author    = "Primozic, T."
,title     = "Estimating expected first passage times using
              multilevel {M}onte {C}arlo algorithm"
,school    = "University of Oxford"
,type      = "{MSc} thesis"
,year      = "2011"
}

@incollection{rg12
,author    = "Rhee, C.-H. and Glynn, P.W."
,title     = "A new approach to unbiased estimation for {SDE}s"
,booktitle = "Proceedings of the 2012 Winter Simulation Conference"
,editors   = "Laroque, C. and Himmelspach, J. and Pasupathy, R.
              and Rose, O. and Uhrmacher, A.M."
,publisher = "IEEE"
,year      = "2012"
}

@article{rg15
,author    = "Rhee, C.-H. and Glynn, P.W."
,title     = "Unbiased estimation with square root convergence
              for {SDE} models"
,journal   = "Operations Research"
,volume    = "63"
,number    = "5"
,pages     = "1026-1043"
,year      = "2015"
}

@phdthesis{ricketson14
,author    = "Ricketson, L.F."
,title     = "Two approaches to accelerated {M}onte {C}arlo
              simulation of {C}oulomb collisions"
,school    = "UCLA"
,type      = "{PhD} thesis"
,year      = "2014"
}

@article{rs17
,author    = "Rosenbaum, I. and Staum, J."
,title     = "Multilevel {M}onte {C}arlo metamodeling"
,journal   = "Operations Research"
,volume    = "65"
,number    = "4"
,pages     = "1062-1077"
,year      = "2017"
}

@article{rrdcc14
,author    = "Rosin, M.S. and Ricketson, L.F. and Dimits, A.M.
              and Caflisch, R. and Cohen, B.I."
,title     = "Multilevel {M}onte {C}arlo simulation of {C}oulomb collisions"
,journal   = "Journal of Computational Physics"
,volume    = "247"
,pages     = "140-157"
,year      = 2014
}

@article{sst17
,author    = "Scheichl, R. and Stuart, A. and Teckentrup, A."
,title     = "Quasi-{M}onte {C}arlo and multilevel {M}onte {C}arlo methods for
              computing posterior expectations in elliptic inverse problems"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "5"
,number    = "1"
,pages     = "466-492"
,year      = 2017
}

@incollection{stw13
,author    = "de Schryver, C. and Torruella, P. and Wehn, N."
,title     = "A multi-level {M}onte {C}arlo {FPGA} accelerator for option
              pricing in the {H}eston model"
,booktitle = "Proceedings - Design, Automation and Test in Europe"
,publisher = "ACM"
,pages     = "248-253"
,year      = "2013"
}

@phdthesis{speight07
,author    = "Speight, A.L."
,title     = "A multilevel approach to control variates"
,school    = "Carnegie-Mellon University"
,type      = "{PhD} thesis"
,year      = "2007"
}

@article{speight09
,author    = "Speight, A.L."
,title     = "A multilevel approach to control variates"
,journal   = "Journal of Computational Finance"
,volume    = 12
,pages     = "1-25"
,year      = 2009
}

@article{speight10
,author    = "Speight, A.L."
,title     = "Multigrid techniques in economics"
,journal   = "Operations Research"
,volume    = 58
,number    = 4
,pages     = "1057-1078"
,year      = 2010
}

@phdthesis{sheridan-methven21
,author    = "Sheridan-Methven, O."
,title     = "Nested multilevel {M}onte {C}arlo methods and a modified
              {E}uler-{M}aruyama scheme utilising approximate {G}aussian
	      random variables suitable for vectorised hardware and
	      low-precisions"
,school    = "University of Oxford"
,type      = "{DPhil} thesis"
,year      = "2021"
}

@article{sg24
,author    = "Sheridan-Methven, O. and Giles, M.B."
,title     = "Rounding error using low precision approximate random variables"
,journal   = "SIAM Journal on Scientific Computing"
,volume    = 46
,number    = 4
,pages     = "B502-B526"
,year      = 2024
}

@article{tkh17
,author    = "Taghizadeh, L. and Khodadadian, A. and Heitzinger, C."
,title     = "The optimal multilevel {M}onte-{C}arlo approximation of
              the stochastic drift–diffusion-{P}oisson system"
,journal   = "Computer Methods in Applied Mechanics and Engineering"
,volume    = "318"
,pages     = "739-761"
,year      = 2017
}

@article{tsgu13
,author    = "Teckentrup, A. and Scheichl, R. and Giles, M.B.
              and Ullmann, E."
,title     = "Further analysis of multilevel {M}onte {C}arlo methods
              for elliptic {PDE}s with random coefficients"
,journal   = "Numerische Mathematik"
,volume    = 125
,number    = 3
,pages     = "569-600"
,year      = 2013
}

@incollection{teckentrup12
,author    = "Teckentrup, A."
,title     = "Multilevel {M}onte {C}arlo methods for highly
              heterogeneous media"
,booktitle = "Proceedings of the 2012 Winter Simulation Conference"
,editors   = "Laroque, C. and Himmelspach, J. and Pasupathy, R.
              and Rose, O. and Uhrmacher, A.M."
,publisher = "IEEE"
,year      = "2012"
}

@phdthesis{teckentrup13
,author    = "Teckentrup, A."
,title     = "Multilevel {M}onte {C}arlo methods and
              uncertainty quantification"
,school    = "University of Bath"
,type      = "{PhD} thesis"
,year      = "2013"
}

@phdthesis{turkedjiev13
,author    = "Turkedjiev, P."
,title     = "Numerical methods for backward stochastic differential
              equations of quadratic and locally {L}ipschitz type"
,school    = "Humboldt University"
,type      = "{PhD} thesis"
,year      = "2013"
}

@article{up15
,author    = "Ullmann, E. and Papaioannou, I."
,title     = "Multilevel estimation of rare events"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = "3"
,number    = "1"
,pages     = "922–953"
,year      = "2015"
}

@article{vngp15
,author    = "Vidal-Codina, F. and Nguyen, N.C. and Giles, M.B. and Peraire, J."
,title     = "A model and variance reduction method for computing statistical
              outputs of stochastic elliptic partial differential equations"
,journal   = "Journal of Computational Physics"
,volume    = 297
,pages     = "700-720"
,year      = 2015
}

@article{vngp16
,author    = "Vidal-Codina, F. and Nguyen, N.C. and Giles, M.B. and Peraire, J."
,title     = "An empirical interpolation and model-variance reduction method
              for computing statistical outputs of parametrized stochastic
              partial differential equations"
,journal   = "SIAM/ASA Journal on Uncertainty Quantification"
,volume    = 4
,number    = 1
,pages     = "244–265"
,year      = 2016
}

@article{wg03
,author    = "Ward, A. and Glynn, P.W."
,title     = "A diffusion approximation for a {M}arkovian queue with reneging"
,journal   = "Queueing Systems"
,volume    = 43
,number    = "1-2"
,pages     = "103-128"
,year      = 2003
}

@incollection{xg12
,author    = "Xia, Y. and Giles, M.B."
,title     = "Multilevel path simulation for jump-diffusion {SDE}s"
,publisher = "Springer"
,booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2010"
,editor    = "Plaskota, L. and Wo{\'z}niakowski, H."
,pages     = "695-708"
,year      = "2012"
}

@phdthesis{xia14
,author    = "Xia, Y."
,title     = "Multilevel {M}onte {C}arlo for jump processes"
,school    = "University of Oxford"
,type      = "{DPhil} thesis"
,year      = "2014"
}

@article{xhw20
,author    = "Xu, Z. and He, Z. and Wang, X."
,title     = "Efficient risk estimation via nested multilevel
              quasi-{M}onte {C}arlo simulation"
,journal   = "ArXiv preprint: 2011.11898"
,year      = "2020"
}