论文标题
时空域中的时间对称最佳随机控制问题
Time-symmetric optimal stochastic control problems in space-time domains
论文作者
论文摘要
我们提出了一对伴随的最佳控制问题，这些问题表征了按随机时间间隔定义的一类时间对称的随机过程。相关的PDE是自由型的类型。我们方法的特殊性在于，它涉及两个适合一对过滤的最佳停止时间，传统的增加了一个和彼此的逐渐减少。它们是构造时间对称性的钥匙，可以将其视为“Schrödinger的问题”（1931-32）对时空域的概括。还描述了与“隐藏扩散”概念的关系。
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves two adjoint optimal stopping times adapted to a pair of filtrations, the traditional increasing one and another, decreasing. They are the keys of the time symmetry of the construction, which can be regarded as a generalization of "Schrödinger's problem" (1931-32) to space-time domains. The relation with the notion of "Hidden diffusions" is also described.
