Minimax optimality of Shiryaev-Roberts procedure for quickest drift change detection of a Brownian motion. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Banerjee, Taposh; Moustakides, George V.
• Is Part Of: Sequential analysis. Volume 36:Issue 3(2017)
• Page Start: 355
• Page End: 369
• Publication Date: 2017-07-03
• Subjects: Brownian motion -- drift change detection -- minimax optimality -- quickest change detection -- Shiryaev-Roberts procedure; 62L05 -- 62L10 -- 62L15 -- 62F05 -- 62F15 -- 60G40; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2017.1360088
• Languages: English
• ISSNs: 0747-4946

Abstract

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