Minimax optimality of Shiryaev-Roberts procedure for quickest drift change detection of a Brownian motion

Abstract

ABSTRACTThe problem of detecting a change in the drift of a Brownian motion is considered. The change point is assumed to have a modified exponential prior distribution with unknown parameters. A worst-case analysis with respect to these parameters is adopted leading to a min–max problem formulation. Analytical and numerical justifications are provided toward establishing that the Shiryaev-Roberts procedure with a specially designed starting point is exactly optimal for the proposed mathematical setup.