On confidence intervals for Brownian motion changepoint times

We consider a sequential problem of finding the best confidence interval for a changepoint time of a Brownian motion. Namely, let B= (B sub()t sub()t> or =, slanted]0be a standard Brownian motion defined on a probability space [Omega, [scriptF], P) and let [straighttheta] be an unobservable non-n...

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Bibliographic Details
Published in:Russian mathematical surveys 2016-01, Vol.71 (1), p.159-160
Main Authors: Zhitlukhin, M. V., Muravlev, A. A., Shiryaev, A. N.
Format: Article
Language:English
Subjects:
Brownian motion
Confidence intervals
Disorders
Drift
Mathematical analysis
Probability distribution
Random variables
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Summary:We consider a sequential problem of finding the best confidence interval for a changepoint time of a Brownian motion. Namely, let B= (B sub()t sub()t> or =, slanted]0be a standard Brownian motion defined on a probability space [Omega, [scriptF], P) and let [straighttheta] be an unobservable non-negative random variable which does not depend on B and has a known distribution. Observable is the process X sub()t [mu](t- [straighttheta]) super(+)+ B sub()t t[> or =, slanted] 0, where [mu] [not =] 0 is a known parameter. Thus, at time [straighttheta] a 'disorder' occurs, which is manifested through the change of the drift coefficient from zero to [mu].
ISSN:0036-0279
1468-4829
DOI:10.1070/RM9702