Stability of stochastic dynamic systems of a random structure with Markov switchings in the presence of concentration points

Taras Lukashiv; Igor V. Malyk; Maryna Chepeleva; Petr V. Nazarov

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arXiv · 2305.11735

Stability of stochastic dynamic systems of a random structure with Markov switchings in the presence of concentration points

Taras Lukashiv·Igor V. Malyk·Maryna Chepeleva·Petr V. Nazarov

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Abstract

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system.

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Taras Lukashiv, Igor V. Malyk, Maryna Chepeleva, Petr V. Nazarov. 2023-05-19. Stability of stochastic dynamic systems of a random structure with Markov switchings in the presence of concentration points. https://arxiv.org/abs/2305.11735

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