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This article is cited in 23 scientific papers (total in 23 papers)
Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of Markov Processes with Applications to Quickest Change Detection
M. Pollaka, A. G. Tartakovskiib a Hebrew University of Jerusalem
b University of Southern California
Abstract:
We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval $[0,A]$ as $A\to\infty$. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably standardized) that does not rely on embedding in a regeneration process. We show that under certain conditions the moment generating function of a suitably standardized version of the first exit time converges to that of Exponential (1), and we connect between the standardizing constant and the quasi-stationary distribution (assuming it exists). The results are applied to the evaluation of a distribution of run length to false alarm in change-point detection problems.
Keywords:
Markov process, stationary distribution, quasi-stationary distribution, first exit time, asymptotic exponentiality, change-point problems, CUSUM procedures, Shiryaev-Roberts procedures.
Received: 16.03.2007 Revised: 23.04.2008
Citation:
M. Pollak, A. G. Tartakovskii, “Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of Markov Processes with Applications to Quickest Change Detection”, Teor. Veroyatnost. i Primenen., 53:3 (2008), 500–515; Theory Probab. Appl., 53:3 (2009), 430–442
Linking options:
https://www.mathnet.ru/eng/tvp2444https://doi.org/10.4213/tvp2444 https://www.mathnet.ru/eng/tvp/v53/i3/p500
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Abstract page: | 298 | Full-text PDF : | 136 | References: | 65 |
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