论文标题
随机观察时间的最后成功停止问题
The Last-Success Stopping Problem with Random Observation Times
论文作者
论文摘要
假设在混合二项式过程的随机时间顺序观察到$ n $独立的伯努利试验。任务是通过使用非正式的停止策略来最大化，这是停止最后成功的可能性。我们专注于问题的版本，其中$ k^\ text {th} $试验是成功的，概率$ p_k =θ/（θ+k-1）$，$ n $的先前分布是负二项式，shape参数$ν$。探索高斯高几何功能的属性，我们发现近视停止策略是最佳的，并且仅当$ν\geqθ$时。我们得出公式来评估获胜概率，并讨论大型$ n $的问题的限制形式。
Suppose $N$ independent Bernoulli trials are observed sequentially at random times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. We focus on the version of the problem where the $k^\text{th}$ trial is a success with probability $p_k=θ/(θ+k-1)$ and the prior distribution of $N$ is negative binomial with shape parameter $ν$. Exploring properties of the Gaussian hypergeometric function, we find that the myopic stopping strategy is optimal if and only if $ν\geqθ$. We derive formulas to assess the winning probability and discuss limit forms of the problem for large $N$.
