Stability results for neutral stochastic functional differential equations via fixed point methods

Abstract

In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a necessary and sufficient condition ensuring the asymptotic stability is proved. The assumption does not require neither boundedness or differentiability of the delay functions, nor do they ask for a fixed sign on the coefficient functions. In particular, the results improve some previous ones proved by Guo, Y., Xu, C., & Wu, J. [(2017). Stability analysis of neutral stochastic delay differential equations by a generalisation of Banach’s contraction principle. International Journal of Control, 90, 1555–1560]. Finally, an example is exhibited to illustrate the effectiveness of the proposed results.