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The paper deals with the quickest detection of a change of the drift of the Brownian motion. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the optimal stopping problem for a diffusion Markov process. For this problem the optimal procedure is described and its characteristics are found. We show also that the same procedure is asymptotically optimal for the minimax formulation of the quickest detection problem.

Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings