201609
20190317000005.0
ISI
000354704400004
doi
10.1007/s10543-014-0511-3
ARTICLE
A continuation multilevel Monte Carlo algorithm
2015
2015
34
Journal Articles
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding variance and weak error. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients.
Multilevel Monte Carlo
Monte Carlo
Partial differential equations with random data
Stochastic differential equations
Bayesian inference
Collier, Nathan
250102
Haji-Ali, Abdul-Lateef
270909
241873
Nobile, Fabio
118353
246773
von Schwerin, Erik
226103
Tempone, Raúl
55
2
399-432
BIT Numerical Mathematics
Is New Version Of
https://infoscience.epfl.ch/record/263220
julien.junod@epfl.ch
1856912
http://infoscience.epfl.ch/record/201609/files/2015_Collier_HajiAli_Nobile_eal_BIT_Continuation.pdf
Publisher's version
Publisher's version
252411
CSQI
U12495
oai:infoscience.tind.io:201609
SB
article
GLOBAL_SET
178574
118353
118353
EPFL-ARTICLE-201609
EPFL
REVIEWED
PUBLISHED
ARTICLE