概率最优停止问题

The Problem of Optimal Probability Stopping Time

本文在时齐马氏序列中引入了概率最优停时和(ε,B)概率最优停时的概念,得到了其显式表达式,从而在某种程度上弥补了期望最优时的不足.同时,本文研究了两种停止问题的关系,指出期望最优停时也是概率最优停时的特例,并证明了集合首达时也是一种概率最优时,进一步给出了首达时为有限的等价条件.

This paper introduces the conception of optimal probability time and (ε,B) optimal probablity stopping time for the homogeneous Markov Sequence and obtains their explicit expressions to remedy some shortcoming of the optimal expection time. The relation of two kinds of time is studied. It is proved that the first hit time is an optimal probability time and the equivalent condition of the first hit time is finite.