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October, 1975 Limit Theorems for Extreme Values of Chain-Dependent Processes
G. E. Denzel, G. L. O'Brien
Ann. Probab. 3(5): 773-779 (October, 1975). DOI: 10.1214/aop/1176996264


The principal results of Resnick and Neuts (1970) and Resnick (1971) concerning limiting distributions for the maxima of a sequence of random variables defined on a Markov chain have been extended to denumerable Markov chains. These results apply a fortiori to Markov renewal processes. The method of proof is to show that limit distributions are independent of the initial distribution of the chain and then to apply known results for stationary processes.


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G. E. Denzel. G. L. O'Brien. "Limit Theorems for Extreme Values of Chain-Dependent Processes." Ann. Probab. 3 (5) 773 - 779, October, 1975.


Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0322.60088
MathSciNet: MR386068
Digital Object Identifier: 10.1214/aop/1176996264

Primary: 60K99
Secondary: 60F05 , 60K15

Keywords: Extreme values , limiting distributions , Mixing , Random variables defined on a Markov chain

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 5 • October, 1975
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