Existence, uniqueness and Hyers-Ulam stability of random impulsive stochastic integro-differential equations with nonlocal conditions

Abstract

In this article, we study the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups and resolvent operators in Hilbert spaces. Initially, we prove the existence of mild solutions using Hausdorff measures of noncompactness and Mo¨nch fixed point theorem. Then, we explore the stability results which includes continuous dependence of initial conditions, Hyers-Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, we propose an example to validate the obtained results.

Keywords

• stochastic differential equations
• random impulse
• hyers-ulam stability
• mean-square exponential stability