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|Title:||Simulation of a Space-Time Bounded Diffusion|
|Authors:||Milstein, G. N.|
Tretyakov, M. V.
|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.|
SPACE-TIME BROWNIAN MOTION
THE DIRICHLET PROBLEM FOR EQUATIONS OF PARABOLIC AND ELLIPTIC TYPE
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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