Multilevel Monte Carlo Approximation of Distribution Functions and Densities

被引：44

作者：

Giles, Michael B. ^{[1
]}

Nagapetyan, Tigran ^{[2
]}

Ritter, Klaus ^{[3
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] Fraunhofer ITWM, D-67663 Kaiserslautern, Germany

[3] TU Kaiserslautern, Fachbereich Math, D-67653 Kaiserslautern, Germany

来源：

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION | 2015年 / 3卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

multilevel Monte Carlo; approximation of distribution functions and densities; stochastic differential equations; path-(in) dependent functionals; stopped exit times; smoothing; STOCHASTIC DIFFERENTIAL-EQUATIONS; EULER SCHEME; CONVERGENCE; DIFFUSION;

D O I：

10.1137/140960086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct and analyze multilevel Monte Carlo methods for the approximation of distribution functions and densities of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide a general analysis under suitable assumptions on the weak and strong convergence. We apply the results to smooth path-independent and path-dependent functionals and to stopped exit times of stochastic differential equations (SDEs).

引用

页码：267 / 295

页数：29

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