Abstract Motivated by the practical investigation of a state-dependent quickest detection problem in continuous time, especially for Brownian observations, we propose an asymptotic scheme in discrete time called a quickest detection scheme of an accumulated state-dependent change point. Here the state-dependent means that the priori probability of the change point depends on the current state. We reduce the problem to finding an optimal stopping time of a vector-valued Markov process. We illustrate the scheme via a numerical example.

中文翻译：

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最快检测累积的状态相关变化点

摘要 受连续时间状态相关最快检测问题的实际研究的启发，特别是对于布朗观测，我们提出了一种离散时间的渐近方案，称为累积状态相关变化点的最快检测方案。这里状态相关是指变化点的先验概率取决于当前状态。我们将问题简化为寻找向量值马尔可夫过程的最佳停止时间。我们通过一个数值例子来说明这个方案。