标题： 极小化极大维纳序贯检测问题 显示英文标题

标题： The Minimax Wiener Sequential Testing Problem

摘要： 考虑一条一维扩散的样本路径，其中已知扩散系数，并且漂移可能取两个值之一：$\mu_0$或$\mu_1$。 假设信噪比（定义为两个可能漂移值之差除以扩散系数）是非恒定的。 给定观测过程的初始状态后，我们考虑了一个最小最大形式的维纳序贯检验问题，用于尽早检测正确的漂移系数，并使错误终端决策的概率最小化。 我们在贝叶斯公式下解决了该问题，在任何关于过程具有漂移$\mu_0$或$\mu_1$的先验概率下，当时间的流逝被线性惩罚时。 在假设信噪比为常数的情况下，我们得到了最不利分布的显式公式。 显示英文摘要

摘要： Consider the sample path of a one-dimensional diffusion for which the diffusion coefficient is given and where the drift may take on one of two values: $\mu_0$ or $\mu_1$. Suppose that the signal-to-noise ratio (defined as the difference between the two possible drifts divided by the diffusion coefficient) is non-constant. Given an initial state for the observed process, we consider a minimax formulation of the Wiener sequential testing problem for detecting the correct drift coefficient as soon as possible and with minimal probabilities of incorrect terminal decisions. We solve the problem in the Bayesian formulation, under any prior probabilities of the process having drift $\mu_0$ or $\mu_1$, when the passage of time is penalized linearly. In the case where the signal-to-noise ratio is assumed constant, we obtain an explicit formula for the least favorable distribution.