Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111232
Title: The Simplest Random Walks for the Dirichlet Problem
Authors: Milstein, G. N.
Tretyakov, M. V.
Issue Date: 2003
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Citation: Milstein G. N. The Simplest Random Walks for the Dirichlet Problem / G. N. Milstein, M. V. Tretyakov // Theory of Probability and its Applications. — 2003. — Vol. 47. — Iss. 1. — P. 53-68.
Abstract: The Dirichlet problem for both parabolic and elliptic equations is considered. A solution of the corresponding characteristic system of stochastic differential equations is approximated in the weak sense by a Markov chain. If a state of the chain comes close to the boundary of the domain in which the problem is considered, then in the next step the chain either stops on the boundary or goes inside the domain with some probability due to an interpolation law. An approximate solution of the Dirichlet problem has the form of expectation of a functional of the chain trajectory. This makes it possible to use the Monte Carlo technique. The proposed methods are the simplest ones because they are based on the weak Euler approximation and linear interpolation. Convergence theorems, which give accuracy orders of the methods, are proved. Results of some numerical tests are presented.
Keywords: DIRICHLET PROBLEM FOR PARABOLIC AND ELLIPTIC EQUATIONS
MARKOV CHAINS
PROBABILISTIC REPRESENTATIONS
RANDOM WALKS
WEAK APPROXIMATION OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS
URI: http://hdl.handle.net/10995/111232
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 0037265529
ISSN: 0040-585X
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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