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Explicit conditions for asymptotic stability of stochastic Liénard-type equations with Markovian switching |
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| Authors: | Liqin Zhao Fubao Xi |
| Affiliation: | a School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China b Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China |
| Abstract: | This paper deals with the boundedness in probability and convergence for solutions of stochastic Liénard-type equations. Some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained. We also show that white noise can affect the boundedness of corresponding deterministic Liénard equations. |
| Keywords: | Stochastic Lié nard-type equation Boundedness Convergence LaSalle theorem Generalized Itô 's formula |
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