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

Taposh Banerjee; George V. Moustakides

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arXiv · 1610.02680

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

Taposh Banerjee·George V. Moustakides

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Abstract

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.

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Taposh Banerjee, George V. Moustakides. 2016-10-09. Minimax Optimality of Shiryaev-Roberts Procedure for Quickest Drift Change Detection of a Brownian motion. https://arxiv.org/abs/1610.02680

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