Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 407352, 11 pages
doi:10.1155/2008/407352
Fixed points and stability in neutral stochastic differential equations with variable delays
Meng Wu1
, Nan-Jing Huang1
and Chang-Wen Zhao3
1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
3College of Business and Management, Sichuan University, Chengdu, Sichuan 610064, China
Abstract
We consider the mean square asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are also given to illustrate our results.