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.
Publié le : 1999-08-14
Classification:
Space-time Brownian motion,
random walk,
mean-square approximation,
the Dirichlet problem for equations of parabolic and elliptic type,
60H10,
60J15,
65U05
@article{1029962812,
author = {Milstein, G. N. and Tretyakov, M. V.},
title = {Simulation of a space-time bounded diffusion},
journal = {Ann. Appl. Probab.},
volume = {9},
number = {1},
year = {1999},
pages = { 732-779},
language = {en},
url = {http://dml.mathdoc.fr/item/1029962812}
}
Milstein, G. N.; Tretyakov, M. V. Simulation of a space-time bounded diffusion. Ann. Appl. Probab., Tome 9 (1999) no. 1, pp. 732-779. http://gdmltest.u-ga.fr/item/1029962812/