College of Mathematics
Jilin University
Changchun 130012, China
email: stluss@outlook.com
College of Mathematics
Jilin University
Changchun, 130012, China
email: xueyang@jlu.edu.cn
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.2023.01
Show me the PDF file (355 KB), TEX file for this article.
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Shuaishuai Lu College of Mathematics Jilin University Changchun 130012, China email: stluss@outlook.com |
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Xue Yang College of Mathematics Jilin University Changchun, 130012, China email: xueyang@jlu.edu.cn |
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