Second-order neutral impulsive stochastic evolution equations with infinite delay: existence, uniqueness and averaging principle

Abstract

In this paper, a class of second-order neutral impulsive stochastic evolution equations with infinite delay driven by fractional Brownian motion and Poisson jumps is considered. We utilise the Carathéodory approximation technique, the Burkhölder–Davies–Gundy inequality and the Gronwall inequality to present the existence and uniqueness of mild solutions for the addressed system under Carathéodory conditions. Furthermore, we derive an averaging principle for the proposed system which is approximated by the simplified equation in the sense of mean square. Finally, an application is used to illustrate the obtained theoretical results.