Levy Approximation of Impulsive Recurrent Process with Markov Switching

TL;DR

This paper proves the weak convergence of impulsive recurrent processes with Markov switching using Levy approximation, employing a modified method based on singular perturbation solutions instead of ergodic theorems.

Contribution

It introduces a novel approach to establish Levy approximation for impulsive processes with Markov switching, extending existing methods with a singular perturbation technique.

Findings

Weak convergence of impulsive recurrent processes with Markov switching established.

A modified method for relative compactness using singular perturbation solutions.

Advances the theoretical understanding of Levy approximation in stochastic processes.

Abstract

In this paper, the weak convergence of impulsive recurrent process with Markov switching in the scheme of Levy approximation is proved. For the relative compactness, a method proposed by R. Liptser for semimartingales is used with a modification, where we apply a solution of a singular perturbation problem instead of an ergodic theorem.