无限维HJB方程与随机发展方程的广义Fukushima分解最优控制
HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition
摘要：
研究了可分希尔伯特空间中由抽象发展方程驱动的随机最优控制问题。通过将状态方程的温和解识别为$ν$ -弱Dirichlet过程，证明了该值过程是一个实弱Dirichlet过程.相应的分解的唯一性被用来证明一个验证定理。通过这种技术，所需的几个假设是温和的，比以前的贡献有关的非正则解的Hamilton-Jacobi-Bellman方程。
英文摘要：
A stochastic optimal control problem driven by an abstract evolution equation in a separable Hilbert space is considered. Thanks to the identification of the mild solution of the state equation as $ν$-weak Dirichlet process, the value processes is proved to be a real weak Dirichlet process. The uniqueness of the corresponding decomposition is used to prove a verification theorem. Through that technique several of the required assumptions are milder than those employed in previous contributions about non-regular solutions of Hamilton-Jacobi-Bellman equations.
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