Asymptotic Dissipativity for Merged Stochastic Evolutionary Systems with Markov Switchings and Impulse Perturbations under Conditions of Lévy Approximation

Abstract

Conditions for asymptotic dissipativity are established for the merged system of stochastic differential equations with Markov switchings and impulse perturbations under conditions of Levy approximation. In particular, it is analyzed how the behavior of the boundary process depends on the pre-limiting normalization of a stochastic evolution system in the ergodic Markovian environment under the conditions of Levy approximation.