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Optimality of the 2-CUSUM drift equalizer rules for detecting two-sided alternatives in the Brownian motion model

Part of: Game theory Sequential methods Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Olympia Hadjiliadis
Olympia Hadjiliadis*
Affiliation:
Columbia University
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Abstract

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This work employs the Brownian motion model in which observations are taken sequentially. The objective is to detect a two-sided change in the constant drift by means of a stopping rule. As a performance measure, an extended Lorden criterion is used. The goal is to minimize the worst-case detection delay subject to a constraint in the frequency of false alarms. In a companion paper, attention is drawn to a first category of 2-CUSUM rules for which the harmonic mean rule holds. It is further seen that a special class of 2-CUSUM stopping rules within this category, called drift equalizer rules, perform strictly better than non-equalizer rules, according to this specific performance measure.

Keywords

Sequential change detectiondetection delayCUSUMtwo-sided CUSUM

MSC classification

Primary: 62L15: Optimal stopping
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 91A60: Probabilistic games; gambling
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1183 - 1193
Copyright
© Applied Probability Trust 2005 

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