Abstract

We consider an optimal control problem where a Brownian motion with drift is sequentially observed and the sign of the drift coefficient changes at jump times of a symmetric two-state Markov process. The Markov process itself is not observable, and the problem consists of finding a {−1, 1}-valued process that tracks the unobservable process as closely as possible. We present an explicit construction of such a process.

中文翻译：

---

布朗噪声下不可观测的二态马尔可夫过程的顺序跟踪

摘要

我们考虑一个最优控制问题，在该问题中顺序观察到具有漂移的布朗运动，并且在对称两态马尔可夫过程的跳跃时间处，漂移系数的符号会发生变化。马尔可夫过程本身是不可观察的，问题在于找到一个{-1，1}值的过程，该过程尽可能密切地跟踪不可观察的过程。我们提出了这样一个过程的显式构造。