global lipschitz condition

In this paper, we derive the existence and the uniqueness theorem for the mild solution of nonlinear stochastic differential equations dX=[AX+f(X)]dt+[BX+g(X)]dW in infinite dimensions under non-Lipschitzian condition by investigating the convergence of the successive approximation.

通过构造收敛的逼近列的方法给出了非李普希茨条件下无穷维随机微分方程dX=[AX+f(X)]dt+[BX+g(X)]dW的适度解的存在唯一性定理。