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Stability of maxima of random variables defined on a Markov chain

Published online by Cambridge University Press:  01 July 2016

Sidney I. Resnick
Sidney I. Resnick*
Affiliation:
Technion—Israel Institute of Technology, Haifa
*
∗ Present address: Stanford University.
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Abstract

Consider maxima M n of a sequence of random variables defined on a finite Markov chain. Necessary and sufficient conditions for the existence of normalizing constants B n such that are given. The problem can be reduced to studying maxima of i.i.d. random variables drawn from a finite product of distributions πi=1 m H i (x). The effect of each factor H i (x) on the behavior of maxima from πi=1 m H i is analyzed. Under a mild regularity condition, B n can be chosen to be the maximum of the m quantiles of order (1 - n -1) of the H's.

Keywords

SEMI-MARKOV PROCESSESRELATIVE STABILITY OF MAXIMADISTRIBUTIONS WITH RAPIDLY VARYING TAILSPRODUCTS OF DISTRIBUTIONSMARKOV CHAINS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 4 , Issue 2 , August 1972 , pp. 285 - 295
Copyright
Copyright © Applied Probability Trust 1972 

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Footnotes

Research carried out at Purdue University and supported by the National Science Foundation Graduate Traineeship Program and by N.S.F. Contract GP-7631.

References

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