We study extensions to higher dimensions of the classical Bayesian sequential testing and detection problems for Brownian motion. In the main result, we show that, for a large class of problem formulations, the cost function is unilaterally concave. This concavity result is then used to deduce structural properties for the continuation and stopping regions in specific examples.

中文翻译：

---

多维顺序检测

我们研究对布朗运动的经典贝叶斯序列测试和检测问题的更高维度的扩展。在主要结果中，我们表明，对于一大类问题表述，成本函数是单边凹的。然后使用该凹度结果来推断特定示例中的延续和停止区域的结构特性。