Compensating Operator and Weak Convergence of Semi-Markov Process to the Diffusion Process without Balance Condition

Abstract

Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process.

Optimal Control of Stochastic Dynamic Systems of a Random Structure with Poisson Switches and Markov Switching

“…Such situations are adequately described by taking into account the term in the equation of motion, which is the integral of the Poisson measure. Stochastic systems with semi-Markov switching were introduced in [23]. In this paper, the conditions of weak convergence of semi-Markov random evolutions to the diffusion process are considered.…”