## The Annals of Applied Probability

### Robustness of the N-CUSUM stopping rule in a Wiener disorder problem

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab. Volume 25, Number 6 (2015), 3405-3433.

Dates
Revised: October 2014
First available in Project Euclid: 1 October 2015

https://projecteuclid.org/euclid.aoap/1443703778

Digital Object Identifier
doi:10.1214/14-AAP1078

Mathematical Reviews number (MathSciNet)
MR3404640

Zentralblatt MATH identifier
1328.62500

#### Citation

Zhang, Hongzhong; Rodosthenous, Neofytos; Hadjiliadis, Olympia. Robustness of the N -CUSUM stopping rule in a Wiener disorder problem. Ann. Appl. Probab. 25 (2015), no. 6, 3405--3433. doi:10.1214/14-AAP1078. https://projecteuclid.org/euclid.aoap/1443703778

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