Sequential tracking of an unobservable two-state Markov process under Brownian noise

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2019-08-03 DOI:10.1080/07474946.2021.1847924

A. Muravlev, M. Urusov, M. Zhitlukhin

引用次数: 1

Abstract

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.

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布朗噪声下不可观测两态马尔可夫过程的顺序跟踪

摘要我们考虑了一个最优控制问题，其中连续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漂移系数的符号发生变化。马尔可夫过程本身是不可观测的，问题包括找到一个{−1，1}值的过程，该过程尽可能密切地跟踪不可观测过程。我们提出了这样一个过程的明确结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.