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

Author 
yaroslav.chab@gmail.com^{1}, nikitin2505@gmail.com^{2}, ulyana.himka@gmail.com^{3}
1) Politechnika Lubelska, Lublin, Poland; 2) Taras Shevchenko National University of Kyiv, Kyiv, Ukraine; 3) Ivan Franko National University of Lviv, Lviv, Ukraine

Abstract 
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 prelimiting normalization of the stochastic evolutionary system in the ergodic
Markov environment.

Keywords 
random evolution; Levy’s approximation conditions; point of equilibrium of the quality criterion

DOI 
doi:10.30970/ms.52.1.96104

Reference 
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Pages 
96104

Volume 
52

Issue 
1

Year 
2019

Journal 
Matematychni Studii

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