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)+∫~T_tf(s,x(s),y(s))ds+g(s,x(s),y(s))dW(s)=ξ,0≤t≤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 esti- mates of the solutions and the continuous dependence on terminal value of the nonlinear stochastic differential equation are also obtained.