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Continuous Dependence of the Solution of A Stochastic Differential Equation With Nonlocal Conditions

Abstract

In this paper we are concerned with a nonlocal problem of a stochastic differential equation that contains a Brownian motion. The solution contains both of mean square Riemann and mean square Riemann-Steltjes integrals, so we study an existence theorem for unique mean square continuous solution and its continuous dependence of the random data X₀ and the (non-random data) coefficients of the nonlocal condition ak. Also, a stochastic differential equation with the integral condition will be considered.

El-Sayed AMA*, Abd-El-Rahman RO, El-Gendy M

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