Continuous Dependence of the Solution of A Stochastic DifferentialEquation With Nonlocal Conditions

[摘要] 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.

[关键词] Integral condition;Brownian motion;Unique mean Square solution;Continuous dependence;Random data;Non- Random data;Integral condition