properties of the impulse perturbation process under Levy approximation conditions with the point of equilibrium of the quality criterion, Mat. Stud. 52 (2019), 96-104. For the system of stochastic differential equations with Markov switchings and impulse disturbance in the conditions of Levy approximation of a single equilibrium point of the quality criterion, limiting generators of the impulse process and dynamical system are constructed. In particular, we discuss how the behavior of the boundary process depends on the pre-limiting normalization of the stochastic evolutionary system in the ergodic Markov environment.
Abstract. This paper considers the random evolution with Markov switching. The resulting limited process is diffusion and depends on the small series parameter. The sufficient conditions of dissipativity of the limited process were obtained. Since the conditions of the Model Limit theorem and dissipativity conditions were set asymptotic dissipativity of the output process.
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