On the dirichlet problem for a class of second order pde systems with small parameter

The Dirichlet problems for a class of singularly perturbed systems of PDE are considered. We use the stochastic representation for solutions of such systems that based on the exit distributions for the Markov process on the phase space where satisfies SDE: is a Wiener process in and the transition probabilities for ve have the form: . The conditions when these solutions converge to the generalized solution of the corresponding degenerate system are found. Some estimates of this convergence are obtained.