ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM

• 成果类型: Article
• 署名作者: Zhang, Hongzhong; Rodosthenous, Neofytos; Hadjiliadis, Olympia
• 署名单位: Columbia University; University of London; Queen Mary University London; City University of New York (CUNY) System; Hunter College (CUNY); City University of New York (CUNY) System; City University of New York (CUNY) System
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1078
• 发表日期: 2015
• 页码: 3405-3433
• 关键词: quickest detection; optimality

摘要

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.