Quickest detection of a minimum of disorder times

Erhan Bayraktar, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

A multi-source quickest detection problem is considered. Assume there are two independent Poisson processes X1 and X2 with disorder times θ1 and θ2, respectively: that is the intensities of X1 and X2 change at random unobservable times θ1 and θ2, respectively. θ1 and θ2 are independent of each other and are exponentially distributed. Define θ θ1 Λ θ2 = min{θ1, θ2}. For any stopping time τ that is measurable with respect to the filtration generated by the observations define a penalty function of the form Rτ = ℙ(τ < θ) + c double-struck E sign [(τ - θ)+], where c > 0 and (τ - θ)+ is the positive part of τ - θ. It is of interest to find a stopping time τ that minimizes the above performance index. Since both observations X1 and X2 reveal information about the disorder time τ, even this simple problem is more involved than solving the disorder problems for X1 and X2 separately. This problem is formulated in terms of a two dimensional sufficient statistic, and the corresponding optimal stopping problem is examined. Using a suitable single jump operator, this problem is solved explicitly.

Original languageEnglish (US)
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages326-331
Number of pages6
DOIs
StatePublished - Dec 1 2005
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: Dec 12 2005Dec 15 2005

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Other

Other44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
CountrySpain
CitySeville
Period12/12/0512/15/05

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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    Bayraktar, E., & Poor, H. V. (2005). Quickest detection of a minimum of disorder times. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 326-331). [1582176] (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1582176