Asymptotic Exponentiality of the Distribution of First Exit times for a Class of Markov Processes with Applications to Quickest Change Detection

نویسندگان

  • Moshe Pollak
  • Alexander Tartakovsky
  • MOSHE POLLAK
  • ALEXANDER G. TARTAKOVSKY
چکیده

We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval [0, A] as A → ∞. 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 ofExponential(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.

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تاریخ انتشار 2006