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

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.

KEYWORDS:

• Change point detection
• optimal stopping
• optimal switching
• sequential tracking

SUBJECT CLASSIFICATIONS:

• 62L10
• 62L15
• 60G40

DISCLOSURE

The authors have no conflicts of interest to report.

FUNDING

The research was supported by the Russian Science Foundation, Project 19-11-00290.