Continuous Dependence of the Solution of A Stochastic Differential Equation With Nonlocal ConditionsEl-Sayed AMA1*, Abd-El-Rahman RO2, El-Gendy M2
- Corresponding Author:
- El-Sayed AMA
Faculty of Science Alexandria University, Egypt
E-mail: [email protected]
Received date: 21/01/2016; Accepted date: 14/04/2016; Published date: 18/04/2016
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.