On the sequential testing and quickest change-point detection problems for Gaussian processes. Issue 8 (17th November 2017)

• Record Type: Journal Article
• Authors: Gapeev, Pavel V.; Stoev, Yavor I.
• Is Part Of: Stochastics. Volume 89:Issue 8(2017)
• Page Start: 1143
• Page End: 1165
• Publication Date: 2017-11-17
• Subjects: Sequential testing -- quickest change-point (disorder) -- likelihood ratio -- time-inhomogeneous diffusion process -- optimal stopping problem -- curved boundary -- free boundary problem -- a change-of-variable formula with local time on curves -- fractional Brownian motion -- fundamental martingale; Primary: 60G40 -- 60J60 -- 34K10 -- Secondary: 62M20 -- 62C10 -- 62L15; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2017.1284222
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : We study the sequential hypothesis testing and quickest change-point (disorder) detection problems with linear delay penalty costs for certain observable time-inhomogeneous Gaussian diffusions and fractional Brownian motions. The method of proof consists of the reduction of the initial problems into the associated optimal stopping problems for one-dimensional time-inhomogeneous diffusion processes and the analysis of the associated free boundary problems for partial differential operators. We derive explicit estimates for the Bayesian risk functions and optimal stopping boundaries for the associated weighted likelihood ratios and obtain their exact asymptotic growth rates under large time values.