Stability of sets of stochastic functional differential equations with impulse effect

Advances in Difference Equations

Yan Xu¹  Zhimin He² 

[1] School of Mathematics and Statistics, Central South University, Changsha, People’s Republic of China

关键词: stability of sets;    Brownian motion;    stochastic functional differential equations;    impulse;    Lyapunov function;    Razumikhin methods;    34K20;    34K45;    34K50;   

DOI  :  10.1186/s13662-015-0551-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the stability of sets for a class of impulsive stochastic functional differential equations. By employing piecewise continuous Lyapunov functions with Razumikhin methods, some sufficient conditions are established to guarantee the stability of sets of impulsive stochastic functional differential equations and we also show that the impulses play an important role in the stability of stochastic functional differential equations. Three examples are presented to illustrate the effectiveness of the results obtained.

【 授权许可】

CC BY