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,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 = "to appear"
,year = "2022"
}
@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"
}
@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 = ""
,number = ""
,pages = ""
,year = "2018"
}
@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"
,series = "Lecture Notes in Computational Science and Engineering"
,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
,number = 2
,pages = "151-175"
,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
,pages = "317-341"
,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
,pages = "229-254"
,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
,pages = "449-474"
,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
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@incollection{inr13
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@phdthesis{kronsbein12
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{M}onte {C}arlo approach on {FPGA}s"
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@phdthesis{ricketson14
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@incollection{stw13
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}
@phdthesis{speight07
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@phdthesis{sheridan-methven20
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heterogeneous media"
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,year = "2012"
}
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uncertainty quantification"
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equations of quadratic and locally {L}ipschitz type"
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@phdthesis{xia14
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}