TY - GEN

T1 - Quickest detection of a minimum of disorder times

AU - Bayraktar, Erhan

AU - Poor, H. Vincent

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33847180575&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847180575&partnerID=8YFLogxK

U2 - 10.1109/CDC.2005.1582176

DO - 10.1109/CDC.2005.1582176

M3 - Conference contribution

AN - SCOPUS:33847180575

SN - 0780395689

SN - 9780780395688

T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

SP - 326

EP - 331

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

T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Y2 - 12 December 2005 through 15 December 2005

ER -