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On record and inter-record times for a sequence of random variables defined on a Markov chain

Published online by Cambridge University Press:  01 July 2016

Gary Lee Guthrie  and
Paul T. Holmes
Gary Lee Guthrie
Affiliation:
Clemson University
Paul T. Holmes
Affiliation:
Clemson University
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Abstract

The familiar three theorems of Rényi concerning the record times in an i.i.d. sequence of random variables are extended to the record times and inter-record times of a sequence of dependent, non-identically distributed random variables defined on a finite Markov chain. These theorems are the Central Limit Theorem (C.L.T.), the Strong Law of Large Numbers (S.L.L.N.) and the Law of the Iterated Logarithm (L.I.L.). Similar results are also obtained for m-record times, inter-m-record times, and for the continuous parameter situation when observations are taken at the epochs of a Poisson process.

Keywords

RECORD TIMESINTER RECORD TIMESMARKOV CHAINCENTRAL LIMIT THEOREMLAW OF LARGE NUMBERSLAW OF THE ITERATED LOGARITHMM-RECORDS
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 195 - 214
Copyright
Copyright © Applied Probability Trust 1975 

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References

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