非线性倒向随机发展方程之适应解

Adapted Solution of a Backward Nonlinear Stochastic Evolution Equation

讨论了非线性倒向随机发展方程 x_((t))+∫_t^Tf(s,x_((s)),y_((s)))ds+∫_t^Ty_((s))dW_((s))=X 在一组广义Lipschitz 条件局部满足的情况下适应解的局部及整体存在唯一性,同时得到此条件下适应解几乎处处有界的结论。

In this paper,we study the following kind of backward nonlinear stochastic evolution equation X_((t))+∫_t^Tf(s,x_((s)),y_((s))ds+∫_t^Ty_((s))dW_((s))=X Under a rather mild assumption,only a local condition is satified.Local and global existence and uniqueness results are obtained.Where(Ω,F,P,W,F_t)is a stan- dard Wiener process,for any given(x,y),f(·,x·y)is an F_t-adapted process, and X is F_T-measurable.