Asymptotic exponentiality of the distribution of first exit times for a class of markov processes with applications to quickest change detection?

M. Pollak*, A. G. Tartakovsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

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 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.

Original languageEnglish
Pages (from-to)430-442
Number of pages13
JournalTheory of Probability and its Applications
Volume53
Issue number3
DOIs
StatePublished - 2009

Keywords

  • Asymptotic exponentiality
  • Change-point problems
  • Cusum procedures
  • First exit time
  • Shiryaev-roberts procedures

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