Abstract: The problem of Bayes sequential decision rules to hypothesis testing is often reduced to the problem of optimal stopping. In continuous time situation, the existence of Bayes solution is proved by using the general stochastic process theory. In distinguishing among two exponential distributions, the Bayes solutions are found out in different situations as an example, which also shows that the uniqueness of solution does not hold in general.

Key words: stopping time, quasi-left continuity, predictable projection, Bayes decision rule

摘要： 假设检验的Bayes序贯决策问题往往可用最优停止理论解决.利用随机过程的一般理论证明了连续时间情形下上问题Bayes解的存在性。作为一个实例，找出了区分两个指数分布的Bayes解的具体形式，并说明解的唯一性在最一般的条件下不成立。

关键词: 停时, 拟左连续性, 可料投影, Bayes判决法则