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We consider an optimal control problem, where a Brownian motion with drift issequentially observed, and the sign of the drift coefficient changes at jumptimes of a symmetric two-state Markov process. The Markov process itself is notobservable, and the problem consist in finding a {-1,1}-valued process thattracks the unobservable process as close as possible. We present an explicitconstruction of such a process.

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