一类非Lipschitz系数的倒向半线性随机发展方程的适应解

Adapted Solution of a Backward Semi Linear Stochastic Evolution Equation with Non-Lipschitz Coefficients

本文研究如下形式的无穷维空间的倒向半线性随机发展方程x(t)+integral from n=t to T e^(A(s-t))f(s,x(s)),y(s))ds+integral from n=t to T e^(A(s-t))[g(s,x(s))+y(s)]dw(s)=e^(A(T-t))X.在系数f(t,x,y),g(t,x)满足一类非Lipschitz条件下得到了方程局部与整体适应解的存在唯一性.

In this paper, the authors shall study the following infinite-dimensional space＇s backward semi linear stochastic evolution equation x（t）＋^T∫ t e（A（s-t））f（s,x（s））,y（s））ds＋^T∫ t eA（s-t）[g（s,x（s））＋y（s）]dw（s）=e^A（T-t）X.The authors proved the existence and uniqueness of the local and global adapted solutions when the coefficients of the equation satisfy non-Lipschitz assumptions.