Consider a standard Brownian motion in one dimension, having either a zero drift, or a non-zero drift that is randomly distributed according to a known probability law. Following the motion in real time, the problem is to detect as soon as possible and with minimal probabilities of the wrong terminal decisions, whether a non-zero drift is present in the observed motion. We solve this problem for a class of admissible laws in the Bayesian formulation, under any prior probability of the non-zero drift being present in the motion, when the passage of time is penalised linearly.

中文翻译：

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检测布朗运动中随机漂移的存在

考虑一维的标准布朗运动，具有零漂移或根据已知概率定律随机分布的非零漂移。实时跟踪运动，问题是尽快并以最小的错误终端决策概率检测观察到的运动中是否存在非零漂移。我们针对贝叶斯公式中的一类可接受定律解决了这个问题，在运动中存在非零漂移的任何先验概率下，当时间的流逝受到线性惩罚时。