Electron. J. Differential Equations, Vol. 2024 (2024), No. 01, pp. 1-16.

Stability and rate of decay for solutions to stochastic differential equations with Markov switching

Shuaishuai Lu, Xue Yang

Abstract:
In this article, we present the almost sure asymptotic stability and a general rate of decay for solutions to stochastic differential equations (SDEs) with Markov switching. By establishing a suitable Lyapunov function and using an exponential Martingale inequality and the Borel-Cantelli theorem, we give sufficient conditions for the asymptotic stability. Also, we obtain sufficient conditions for the construction of two kinds of Lyapunov functions. Finally give two examples to illustrate the validity of our results.

Submitted July 19, 2023. Published January 3, 2024.
Math Subject Classifications: 60H10, 34D99, 34F05.
Key Words: Almost sure asymptotic stability; Markov switching; exponential Martingale inequality; Lyapunov function; generalized Ito formula.
DOI: 10.58997/ejde.2024.01

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Shuaishuai Lu
College of Mathematics
Jilin University
Changchun 130012, China
email: stluss@outlook.com
Xue Yang
College of Mathematics
Jilin University
Changchun, 130012, China
email: xueyang@jlu.edu.cn

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