J-convergence of switching processes with rare perturbations to diffusion processes with Poisson type jumps

Abstract

In the paper it is studied J-convergence for a special subclass of switching processes, recurrent processes of semi-Markov type (Anisimov,1992, Anisimov and Aliev,1990) both with rare interference of chance and in the case of asymptotically merged external Markov environment, to solutions of differential and stochastic differential equations with Poisson switches.