Samoilenko I.V., Nikitin A.V., Dovhai B.V.
Asymptotic dissipativity for merged stochastic evolutionary systems with markov switchings and impulse perturbations under conditions of Levy aproximations

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 Lévy approximation. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: asymptotic dissipativity, Lévy approximation, random evolution, Differential equations, Dissipativity, Ergodics, Evolutionary system, Impulse perturbations, Markovian environment, Stochastic differential equations, Stochastic evolution, Stochastic systems

Cite:
Samoilenko I.V., Nikitin A.V., Dovhai B.V. (2020). Asymptotic dissipativity for merged stochastic evolutionary systems with markov switchings and impulse perturbations under conditions of Levy aproximations. Cybernetics and Systems Analysis, 56 (3), 60–69. doi: https://doi.org/10.1007/s10559-020-00255-4 http://jnas.nbuv.gov.ua/article/UJRN-0001121519 [In Ukrainian].