Asymptotic properties of the impulse perturbation process under Levy approximation conditions with the point of equilibrium of the quality criterion

Y. M. Chabanyuk1, A. V. Nikitin2, U. T. Khimka3
1) Politechnika Lubelska, Lublin, Poland; 2) Taras Shevchenko National University of Kyiv, Kyiv, Ukraine; 3) Ivan Franko National University of Lviv, Lviv, Ukraine
For the system of stochastic differential equations with Markov switchings and impulse disturbance in the conditions of Levy approximation in the conditions of a single point of equilibrium 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.
random evolution; Levys approximation conditions; point of equilibrium of the quality criterion
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