Sequential tracking of an unobservable two-state Markov process under Brownian noise. Issue 1 (20th January 2021)

• Record Type: Journal Article
• Authors: Muravlev, Alexey; Urusov, Mikhail; Zhitlukhin, Mikhail
• Is Part Of: Sequential analysis. Volume 40:Issue 1(2021)
• Page Start: 1
• Page End: 16
• Publication Date: 2021-01-20
• Subjects: Change point detection -- optimal stopping -- optimal switching -- sequential tracking; 62L10 -- 62L15 -- 60G40; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2021.1847924
• Languages: English
• ISSNs: 0747-4946

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.