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August 1999 Simulation of a space-time bounded diffusion
G. N. Milstein, M. V. Tretyakov
Ann. Appl. Probab. 9(3): 732-779 (August 1999). DOI: 10.1214/aoap/1029962812


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.


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G. N. Milstein. M. V. Tretyakov. "Simulation of a space-time bounded diffusion." Ann. Appl. Probab. 9 (3) 732 - 779, August 1999.


Published: August 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0964.60065
MathSciNet: MR1722281
Digital Object Identifier: 10.1214/aoap/1029962812

Primary: 60H10
Secondary: 60J15 , 65U05

Keywords: mean-square approximation , Random walk , Space-time Brownian motion , the Dirichlet problem for equations of parabolic and elliptic type

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 3 • August 1999
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