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The limiting distribution of the maximum term in a sequence of random variables defined on a markov chain

Published online by Cambridge University Press:  14 July 2016

Augustus J. Fabens  and
Marcel F. Neuts
Augustus J. Fabens
Affiliation:
Boston College, Massachusetts
Marcel F. Neuts
Affiliation:
Purdue University, Lafayette, Indiana
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Summary

Gnedenko's classical work [1] on the limit of the distribution of the maximum of a sequence of independent random variables is extended to the distribution of the maximum of a sequence of random variables defined on a finite Markov chain.

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 3 , December 1970 , pp. 754 - 760
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Gnedenko, B. (1943) Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423–453.Google Scholar
[2] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar