Abstract We look at a Poisson process where the arrival rates change from a known λ1 to a known λ2. Whereas in most of the literature the change-point is abrupt, we model the more realistic assumption that states that the change happens gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early. We conclude with some numerical results.

中文翻译：

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在到达率逐渐变化的情况下监测泊松过程

摘要 我们看一个泊松过程，其中到达率从已知的 λ1 变为已知的 λ2。而在大多数文献中，变化点是突然的，我们对更现实的假设进行建模，该假设表明变化在 η 已知的时间段 η 内逐渐发生。我们计算更改已经开始和完成的概率。我们还考虑了最佳停止规则，假设存在误报成本和提前停止的单位时间成本。我们以一些数值结果作为结论。