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Тезисы докладов

Стохастическое моделирование и методы Монте-Карло

Consider a boundary value problem for a linear system of stochastic differential equations $$ dx(t) = A(t) x(t) dt +Sigma(t) dw(t), quad x(alpha)=x_alpha, quad x(beta)=x_beta, $$ where $x(t)$ is a vector-valued random process, $w(t)$ is a vector of independent standard Wiener processes, $A(t)$ and $Sigma(t)$ are matrices whose elements are piecewise continuous functions, $x_alpha$ and $x_beta$ are non-random vectors. To solve the boundary value problem we propose a new method. The method is based on the Gibbs sampler (see, for example, [1]) and it gives an approximate numerical solution of the boundary value problem after a number of iterations. In contrast to the technique presented in [2] which gives for linear systems an "exact" numerical solution, the proposed method can be simpler generalised for stochastic partial differential equations and non-linear systems. vspace{8mm} 1. G.Winkler, Image analysis, Random Fields and Dynamic Monte Carlo Methods. Springer, Berlin, 1995 vspace{6mm} 2. S.M.Prigarin, Numerical solution of boundary value problems for linear systems of stochastic differential equations // Comp. Mathematics and Math. Physics.- 1998.- V.38, N12.- P.1903-1908

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