Sensitivity analysis for a fractional stochastic differential equation with $$S^{p}$$-weighted pseudo almost periodic coefficients and infinite delay

Abstract

In this paper, we study the parameter sensitivity analysis a class of fractional impulsive stochastic differential equation with \(S^{p}\)-weighted pseudo almost periodic coefficients and infinite delay in Hilbert spaces. Firstly, a more appropriate concept of piecewise \(S^{p}\)-weighted pseudo almost periodic in distribution for stochastic processes of class \(\infty \) is introduced. The existence of piecewise weighted pseudo almost periodic mild solutions in distribution is presented by using \(\alpha \)-order fractional resolvent operator theory, the stochastic analysis techniques and a fixed-point theorem. Secondly, the sensitivity properties of these infinite delay systems under non-Lipschitz conditions is also obtained. Finally, two examples are given for demonstration.