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On exponential limit laws for hitting times of rare sets for Harris chains and processes

Part of: Limit theorems Special processes Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Peter W. Glynn
Peter W. Glynn*
Affiliation:
Stanford University, Department of Management Science and Engineering, Stanford University, Huang Engineering Center 357, Stanford, CA 94305, USA. Email address: [email protected]
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Abstract

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This paper provides a simple proof for the fact that the hitting time to an infrequently visited subset for a one-dependent regenerative process converges weakly to an exponential distribution. Special cases are positive recurrent Harris chains and Harris processes. The paper further extends this class of limit theorems to ‘rewards’ that are cumulated to the hitting time of such a rare set.

Keywords

Hitting timeregenerative processHarris recurrent Markov chainHarris recurrent Markov process

MSC classification

Primary: 60F05: Central limit and other weak theorems 60G70: Extreme value theory; extremal processes 60J05: Discrete-time Markov processes on general state spaces 60J25: Continuous-time Markov processes on general state spaces 60K05: Renewal theory
Type
Part 7. Queueing Theory and Markov Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 319 - 326
Copyright
Copyright © Applied Probability Trust 2011 

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