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The problem of detecting a change in the drift of a Brownian motion isconsidered. The change point is assumed to have a modified exponential priordistribution with unknown parameters. A worst-case analysis with respect tothese parameters is adopted leading to a min-max problem formulation.Analytical and numerical justifications are provided towards establishing thatthe Shiryaev-Roberts procedure with a specially designed starting point isexactly optimal for the proposed mathematical setup.

Minimax Optimality of Shiryaev-Roberts Procedure for Quickest Drift Change Detection of a Brownian motion