The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 25, Number 6 (2015), 3405-3433.
Robustness of the N-CUSUM stopping rule in a Wiener disorder problem
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.
Ann. Appl. Probab., Volume 25, Number 6 (2015), 3405-3433.
Received: October 2013
Revised: October 2014
First available in Project Euclid: 1 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62L10: Sequential analysis 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60] 62C20: Minimax procedures 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
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