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

The 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 towards establishing that the Shiryaev-Roberts procedure with a specially designed starting point is exactly optimal for the proposed mathematical setup.

preprint2016arXivOpen access
Taposh BanerjeeGeorge V. Moustakides
math.ITInformation Theorymath.OCmath.STStatistics Theory
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Open access2 authors5 topics
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Taposh BanerjeeGeorge V. Moustakides

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