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

@inproceedings{Tartakovsky2006AsymptoticEO,
  title={Asymptotic Exponentiality of the Distribution of First Exit times for a Class of Markov Processes with Applications to Quickest Change Detection},
  author={Alexander G. Tartakovsky},
  year={2006}
}
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… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 19 references

Optimal detection of a change in distribution

  • M. POLLAK
  • Ann. Statist
  • 1985
Highly Influential
4 Excerpts

Detecting changes in probabilities of a multi-component process

  • R. A. KHAN
  • Sequential Analysis
  • 1995
Highly Influential
1 Excerpt

Average run lengths of an optimal method of detecting a change in distribution

  • M. POLLAK
  • Ann. Statist
  • 1987
Highly Influential
3 Excerpts

Sequential Analysis: Tests and Confidence Intervals

  • D. SIEGMUND
  • 1985
Highly Influential
3 Excerpts

Nonlinear Renewal Theory in Sequential Analysis

  • M. WOODROOFE
  • 1982
Highly Influential
3 Excerpts

Stochastic Processes in Queuing Theory

  • A. A. BOROVKOV
  • 1976
Highly Influential
1 Excerpt

Random difference equations and renewal theory for products of random matrices

  • H. KESTEN
  • Acta Math
  • 1973
Highly Influential
2 Excerpts

The Theory of Branching Processes

  • T. E. HARRIS
  • 1963
Highly Influential
1 Excerpt

Continuous inspection schemes. Biometrika

  • E. S. PAGE
  • 1954
Highly Influential
1 Excerpt

Similar Papers

Loading similar papers…