The solving of boundary value problems by numerical integration of stochastic equations Original Research Article

We will consider two boundary value problems with Dirichlet and Neumann boundary conditions for the equations of parabolic type. Probabilistic representations of solutions of these problems are connected with stochastic differential systems. For realization of the representations we construct Markov chains which weakly approximate the solution of these systems. Unlike usual weak approximations here we are concerned with the certain boundedness of the simulated increments of Markov chains which are necessary to solve the boundary value problems. Most results obtained here can be extended to elliptic equations.