Sequential tracking of an unobservable two-state Markov process under Brownian noise. Issue 1 (20th January 2021) - Muravlev, Alexey; Urusov, Mikhail; Zhitlukhin, Mikhail
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.