Adapted solution of a backward semilinear stochastic evolution equation
Adapted solution of a backward semilinear stochastic evolution equation
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DOI：
10.1080/07362999108809250
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发表时间：
1991
影响因子：
1.3
通讯作者：
Ying Hu;S. Peng
中科院分区：
文献类型：
--
作者：
Ying Hu;S. Peng
设K和H是两个可分的Hilbert空间，是一个圆柱Wiener过程，K中的值定义在一个概率空间上，表示它的自然滤子。给定，我们寻找一个适应过程对，其值在H中，分别定义在§1）中，它解一个后向形式的半线性随机发展方程：其中A是H上C 0-半群{eAt }的无穷小生成元.该方程的精确含义是该方程的线性化版本出现在无限维随机最优控制理论中，作为伴随过程满足的方程。我们也给出了以下倒向随机偏微分方程的结果：
Let K and H be two separable Hilbert spaces and be a cylindrical Wiener process with values in K defined on a probability space denote its natural filtration. Given , we look for an adapted pair of process with values in H and respectively is defined in §1),which solves a semilinear stochastic evolution equation of the backward form: where A is the infinitesimal generators of a C 0-semigroup {eAt } on H. The precise meaning of the equation is A linearized version of that equation appears in infinite-dimensional stochastic optimal control theory as the equation satisfied by the adjoint process. We also give our results to the following backward stochastic partial differential equation: