Differential equations with small stochastic summands under the Levy approximating conditions

Abstract

The proposed methods enable us to study a model of stochastic evolution that includes Markov switchings and to identify the diffusion component and big jumps of perturbing process in the limiting equation. Big jumps of this type may describe rare catastrophic events in different applied problems. We consider the case where the perturbation of the system is determined by an impulse process in the nonclassical approximation scheme. Special attention is given to the asymptotic behavior of the generator of the analyzed evolutionary system.