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Abstract
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We study the quickest detection problem of a sudden change in the arrival of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable time. Our objective is to determine the disorder time as soon as possible. The detection problem is shown to admit finite dimensional sufficient statistic if the new rate ha a discrete distribution with finitely many atoms. Furthermore, the detection problem is cast as a discounted optimal stopping problem for a finite-dimensional piece-wise deterministic Markov process. We study the case of Bernoulli distribution in more detail. Instead of trying to tackle the free boundary problem associated with an integro-differential operator, we solve the problem by constructing an exponentially converging sequence of functions using the iteration of an appropriately defined single-jump operator. This is joint work with Savas Dayanik and Ioannis Karatzas |
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