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arXiv · 1908.01162

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

Alexey Muravlev·Mikhail Urusov·Mikhail Zhitlukhin
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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 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.

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Alexey Muravlev, Mikhail Urusov, Mikhail Zhitlukhin. 2019-08-03. Sequential tracking of an unobservable two-state Markov process under Brownian noise. https://arxiv.org/abs/1908.01162

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