Exponential stability for neutral stochastic partial integro-differential equations of second order with Poisson jumps

Abstract

This paper studies the existence, uniqueness and the exponential stability in $p$-th moment of the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. The existence and uniqueness of the mild solution of neutral second order stochastic differential equation are first established by means of Banach fixed point principle and stochastic analysis. The exponential stability in the $p$-th moment for mild solution to impulsive neutral stochastic integro-differential equations with Poisson jump is obtained by establishing an integral inequality.