Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111671
Title: Simulation of a Space-Time Bounded Diffusion
Authors: Milstein, G. N.
Tretyakov, M. V.
Issue Date: 1999
Publisher: Institute of Mathematical Statistics
Institute of Mathematical Statistics
Citation: Milstein G. N. Simulation of a Space-Time Bounded Diffusion / G. N. Milstein, M. V. Tretyakov // Annals of Applied Probability. — 1999. — Vol. 9. — Iss. 3. — P. 732-779.
Abstract: Mean-square approximations, which ensure boundedness of both time and space increments, are constructed for stochastic differential equations in a bounded domain. The proposed algorithms are based on a space-time discretization using a random walk over boundaries of small space-time parallelepipeds. To realize the algorithms, exact distributions for exit points of the space-time Brownian motion from a space-time parallelepiped are given. Convergence theorems are stated for the proposed algorithms. A method of approximate searching for exit points of the space-time diffusion from the bounded domain is constructed. Results of several numerical tests are presented.
Keywords: MEAN-SQUARE APPROXIMATION
RANDOM WALK
SPACE-TIME BROWNIAN MOTION
THE DIRICHLET PROBLEM FOR EQUATIONS OF PARABOLIC AND ELLIPTIC TYPE
URI: http://hdl.handle.net/10995/111671
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 0033249376
ISSN: 1050-5164
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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