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Limit theorems for sums of chain-dependent processes

Published online by Cambridge University Press:  14 July 2016

G. L. O'Brien
G. L. O'Brien*
Affiliation:
York University, Downsview, Ontario
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Abstract

Chain-dependent processes, also called sequences of random variables defined on a Markov chain, are shown to satisfy the strong law of large numbers. A central limit theorem and a law of the iterated logarithm are given for the case when the underlying Markov chain satisfies Doeblin's hypothesis. The proofs are obtained by showing independence of the initial distribution of the chain and by then restricting attention to the stationary case.

Keywords

MARKOV CHAINSTATIONARY SEQUENCESTRONG LIMIT LAWSCENTRAL LIMIT THEOREM
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 582 - 587
Copyright
Copyright © Applied Probability Trust 1974 

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References

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