Qualitative Behaviour of Stochastic Integro-differential Equations with Random Impulses

Abstract

AbstractIn this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups in Hilbert spaces via resolvent operators. Initially, we prove the existence of mild solution for the system is established by using Mönch fixed point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results includes continuous dependence of solutions on initial conditions, exponential stability and Hyers–Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results.