Continuous dependence of the solution of a stochastic differential equation with nonlocal conditions
Authors :
A. M. A. El-Sayed a,∗ , R. O. Abd-El-Rahman b and M. El-Gendy c
Author Address :
a,b,c Department of Mathematics, College of science, Alexandria university, Egypt.
*Corresponding author.
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 $X_0$ and the (non-random data) coefficients of the nonlocal condition $a_k$. Also, a stochastic differential equation with the integral condition will be considered.
Keywords :
Integral condition, Brownian motion, unique mean square solution, continuous dependence, random data, non-random data, integral condition.
DOI :
Article Info :
Received : January 10, 2016; Accepted : July 21, 2016.