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

08/03/2019

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by   Alexey Muravlev, et al.

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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 consist in finding a -1,1-valued process that tracks the unobservable process as close as possible. We present an explicit construction of such a process.