非线性倒向随机发展方程之适应解
Adapted Solution of a Backward Nonlinear Stochastic Evolution Equation
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摘要: 讨论了非线性倒向随机发展方程x(t)+∫tTf(s,x(s),y(s))ds+∫tTy(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。Abstract: In this paper,we study the following kind of backward nonlinear stochastic evolution equation x(t)+∫tTf(s,x(s),y(s))ds+∫tTy(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,Ft)is a stan-dard Wiener process,for any given(x,y),f(·,x·y)is an Ft-adapted process, and X is Ft-measurable.
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