Existence and Ulam-Hyers-Rassias Stability of Stochastic Differential Equations with Random Impulses

Abstract

In this paper, we investigate the existence and Ulam-Hyers-Rassias stability of solutions for stochastic differential equations with random impulses. Based on the Krasnoselskii’s fixed point theorem, we perform investigations on the existence of solutions to the system of stochastic differential equations with random impulses. We apply the integral inequality of Gronwall type to the equations and study their Ulam-Hyers-Rassias stability.