Existence of solutions and stability for impulsive neutral stochastic functional differential equations

Abstract

In this paper we prove some results on the existence of solutions and the mean square asymptotic stability for a class of impulsive neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a sufficient condition ensuring the asymptotic stability is proved. The assumptions do not impose any restrictions neither on boundedness nor on the differentiability of the delay functions. In particular, the results improve some previous ones in the literature. Finally, an example is exhibited to illustrate the effectiveness of the results.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Junta de AndalucíaEuropean Mathematical Societ