Ulam-Hyers-Rassias stability of a nonlinear stochastic Ito-Volterra integral equation

Abstract

In this paper, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam-Hyers and in the sense of Ulam-Hyers-Rassias for the following stochastic integral equation Xt = ξt + ∫ t 0 A(t,s,Xs)ds+ ∫ t 0 B(t,s,Xs)dWs, where ∫ t 0 B(t,s,Xs)dWs is Ito integral.