TY - GEN
T1 - Quickest detection of a minimum of disorder times
AU - Bayraktar, Erhan
AU - Poor, H. Vincent
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.
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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 -