限制停时类上最优停时问题

摘要

We generalize the framework of [18] for optimal stopping time problem to allow a certain restricted class of stopping times.By using classical results in probability theory on families of random variables indexed by a restricted family of stopping times,we prove the existence of an optimal time,give characterizations of the minimal and maximal optimal stopping times,and provide some local properties of the value function family,in concert with all special cases studied previously.%基于文献[18]的框架,讨论以某种特征的限制停时类为指标集的随机变量族的最优停时问题.运用经典的概率理论,本文证明了最优停时的存在性,刻画了最小、最大停时的特征,给出了相应值函数族的局部性质.当然,上述结论与以往在特殊情况下得出的相一致.