Solution of the first boundary-value problem for parabolic equations by integration of stochastic differential equations. (English. Russian original) Zbl 0859.60055

Milstein, G. N.

Theory Probab. Appl. 40, No. 3, 556-563 (1995); translation from Teor. Veroyatn. Primen. 40, No. 3, 657-665 (1993).

A number of methods are presented for constructing a Markov chain with absorption such that the mathematical expectation of a certain functional of chain paths is close to the solution of a general Dirichlet problem for parabolic equations. The Markov chain weakly approximates the solution of the system of stochastic differential equations which is characteristic for the Dirichlet problem. For the methods under consideration, convergence theorems are obtained with the order of accuracy with respect to approximation step.

Reviewer: G.N.Milstein (Berlin)

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

weak approximation of solutions of stochastic differential equations; Dirichlet problem for parabolic equations; convergence theorems