Multilevel Monte Carlo Approximation of Distribution Functions and Densities | Zendy

Michael B. Giles | Zendy; Tigran Nagapetyan | Zendy; Klaus Ritter | Zendy

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Multilevel Monte Carlo Approximation of Distribution Functions and Densities

Author(s) -

Michael B. Giles,

Tigran Nagapetyan,

Klaus Ritter

Publication year - 2015

Publication title -

siam/asa journal on uncertainty quantification

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.094

H-Index - 29

ISSN - 2166-2525

DOI - 10.1137/140960086

Subject(s) - monte carlo method , univariate , mathematics , statistical physics , convergence (economics) , stochastic differential equation , distribution (mathematics) , weak convergence , path (computing) , random variable , mathematical optimization , computer science , mathematical analysis , statistics , multivariate statistics , physics , computer security , economics , asset (computer security) , programming language , economic growth

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)

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