Numerical solution of boundary value problems for stochastic differential equations on the basis of the Gibbs sampler

To solve boundary value problems for linear systems of stochastic
differential equations we propose and justify a numerical method
based on the Gibbs sampler. In contrast to the technique which
yields for linear systems an "exact" numerical solution, the
proposed method is simpler to generalize for stochastic partial
differential equations and nonlinear systems. Such generalizations
are discussed as well.