### Abstract

A multi-source quickest detection problem is considered. Assume there are two independent Poisson processes X^{1} and X^{2} with disorder times θ_{1} and θ_{2}, respectively: that is the intensities of X^{1} and X^{2} change at random unobservable times θ_{1} and θ_{2}, respectively. θ_{1} and θ_{2} are independent of each other and are exponentially distributed. Define θ ^{△} θ_{1} Λ θ_{2} = min{θ_{1}, θ_{2}}. For any stopping time τ that is measurable with respect to the filtration generated by the observations define a penalty function of the form R_{τ} = 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 X^{1} and X^{2} reveal information about the disorder time τ, even this simple problem is more involved than solving the disorder problems for X^{1} and X^{2} 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 language | English (US) |
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Title of host publication | Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 |

Pages | 326-331 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2005 |

Event | 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: Dec 12 2005 → Dec 15 2005 |

### Publication series

Name | Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 |
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Volume | 2005 |

### Other

Other | 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 |
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Country | Spain |

City | Seville |

Period | 12/12/05 → 12/15/05 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

*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