Sequential testing of a Wiener process with costly observations
Sequential testing of a Wiener process with costly observations
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通过昂贵的观察对维纳过程进行顺序测试
DOI：
10.1080/07474946.2018.1427973
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Erik Ekström
中科院分区：
文献类型：
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作者：
Hannah Dyrssen;Erik Ekström
摘要我们考虑对布朗运动漂移的两个简单假设的顺序检验，当对潜在过程的每一次观测都与正代价相关时。在这种对基本进程进行持续监测是不可行的情况下，问题不仅是在给定的观测时间是停止还是继续，而且如果继续的话，还要考虑如何分配下一次观测时间。采用贝叶斯方法，我们证明了值函数可以被刻画为关联算子的唯一不动点，并且它可以用迭代格式来构造。此外，观测时间的最优顺序分布可以用不动点来描述。
ABSTRACT We consider the sequential testing of two simple hypotheses for the drift of a Brownian motion when each observation of the underlying process is associated with a positive cost. In this setting where continuous monitoring of the underlying process is not feasible, the question is not only whether to stop or to continue at a given observation time but also, if continuing, how to distribute the next observation time. Adopting a Bayesian methodology, we show that the value function can be characterized as the unique fixed point of an associated operator and that it can be constructed using an iterative scheme. Moreover, the optimal sequential distribution of observation times can be described in terms of the fixed point.