Stochastic Liénard Equations with State-Dependent Switching

被引：0
|
作者：
Fu-bao XI
G.YIN
机构：
[1] Beijing Key Laboratory on MCAACI,Beijing Institute of Technology
[2] Department of Mathematics,Wayne State University
[3] School of Mathematics,Beijing Institute of Technology
来源：
ActaMathematicaeApplicataeSinica | 2015年 / 31卷 / 04期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
stochastic Li′enard equation; state-dependent switching; strong Feller property; positive Harris recurrence; exponential ergodicity;
D O I：
暂无
中图分类号：
O211.63 [随机微分方程];
学科分类号：
摘要：
This work focuses on stochastic Li′enard equations with state-dependent switching. First, the existence and uniqueness of a strong solution are obtained by successive construction method. Next, strong Feller property is proved by introducing certain auxiliary processes and using the Radon-Nikodym derivatives and truncation arguments. Based on these results, positive Harris recurrence and exponential ergodicity are obtained under the Foster-Lyapunov drift conditions. Finally, examples using van der Pol equations are presented for illustrations, and the corresponding Foster-Lyapunov functions for the examples are constructed explicitly.
引用
收藏
页码：893 / 908
页数：16
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