First Boundary Value Problem for the Equation of the Elliptic Type

As has been pointed out in Section 1.3, one of the ways to solve the first boundary problem is to reduce it to the integral equation satisfying appropriate conditions and to construct an unbiased estimator of its solution on the trajectories of the convergent Markov chain adapted to this integral equation. In Section 1.3 the scheme was realized for the simplest example of the interior Dirichlet problem for the Laplace operator. Here a more complicated and interesting case of an arbitrary elliptic operator with smooth coefficients will be considered.