Multilevel Monte Carlo codes for 2015 Acta Numerica article

My 2015 Acta Numerica article on Multilevel Monte Carlo Methods is available here. Regrettably, the original version of the article had the following errors which are now corrected in the version given above.

To accompany this article, I developed a number of MATLAB codes to illustrate how the mathematical ideas translate into code. These are presented below, but I would recommend that anyone interested in getting into MLMC application development should use my new MLMC software which is available here.

The advantages of the new software are:

It separates the computation from the generation of figures
It is available in MATLAB, C/C++ and Python
The main driver uses a different split of the Mean Square Error between the bias and variance terms, making it slightly more efficient

but for archival purposes I will leave the old software below.

Generic routines:

mlmc_test.m -- a test routine, discussed in Section 3.3 in the paper
mlmc.m -- main MLMC routine, discussed in detail in Section 3.4

MLMC application codes producing figures for the paper:

gbm_euler.m (Section 5.1)
gbm_milstein.m (Section 5.2)
basket.m (Section 5.3)
ellip.m (Section 7)
para.m (Section 7)

To run the first of these, for example, simply download the file and the generic routines above, and then enter the command "gbm_euler" into MATLAB -- internally it will use both mlmc.m and mlmc_test.m

Additional MLMC application codes:

hyp.m -- nonlinear hyperbolic PDE with stochastic boundary data
heston_antithetic.m -- Heston 2-dimensional SDE with and without antithetic treatment
white_noise.m -- parabolic SPDE with additive white noise
sde_adapted.m -- adaptive time-stepping for an SDE
ctmp_adapted.m -- adaptive time-stepping for a continuous-time Markov process example (warning: long runtime)

For further reading on multilevel Monte Carlo research: