Open Access
December 2015 Robustness of the N-CUSUM stopping rule in a Wiener disorder problem
Hongzhong Zhang, Neofytos Rodosthenous, Olympia Hadjiliadis
Ann. Appl. Probab. 25(6): 3405-3433 (December 2015). DOI: 10.1214/14-AAP1078


We study a Wiener disorder problem of detecting the minimum of $N$ change-points in $N$ observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the $N$ change-points. We adopt a min–max approach and consider an extended Lorden’s criterion, which is minimized subject to a constraint on the mean time to the first false alarm. It is seen that, under partial information of the post-change drifts and a general nonsingular stochastic correlation structure in the noises, the minimum of $N$ cumulative sums (CUSUM) stopping rules is asymptotically optimal as the mean time to the first false alarm increases without bound. We further discuss applications of this result with emphasis on its implications to the efficiency of the decentralized versus the centralized systems of observations which arise in engineering.


Download Citation

Hongzhong Zhang. Neofytos Rodosthenous. Olympia Hadjiliadis. "Robustness of the N-CUSUM stopping rule in a Wiener disorder problem." Ann. Appl. Probab. 25 (6) 3405 - 3433, December 2015.


Received: 1 October 2013; Revised: 1 October 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1328.62500
MathSciNet: MR3404640
Digital Object Identifier: 10.1214/14-AAP1078

Primary: 60K35 , 62L10
Secondary: 60G40 , 62C20 , 62L15

Keywords: correlated noise , CUSUM , quickest detection , Wiener disorder problem

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.25 • No. 6 • December 2015
Back to Top