Adapted Solutions and Continuous Dependence for Nonlinear Stochastic Differential Equations with Terminal Condition

In this paper, we consider a nonlinear stochastic differential equation: x(t)+\int_t^Tf(s,x(s),y(s))\mboxds+\int_t^Tg(s,x(s),y(s))\mboxdW(s)=\xi, \qq 0\leq t\leq T,where W is a d-dimensional standard Wiener process. The existence and uniqueness results of the adapted solution under a condition weaker than the Lipschitz one are proved. The moment estimates of the solutions and the continuous dependence on terminal value of the nonlinear stochastic differential equation are also obtained.