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Geometric and exponential decay in derived Markov chains

Published online by Cambridge University Press:  14 July 2016

Herman Callaert
Herman Callaert*
Affiliation:
Center for Operations Research and Econometrics, University of Leuven
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Abstract

It is known [9] that geometric or exponential decay of a Markov chain is preserved under derivation (as defined by Cohen [2]). In this paper we consider the inverse problem, i.e., does a derived Markov chain with a geometrical or exponential decay necessarily arise from a Markov chain having the same property. For a large class of Markov chains (including time reversible chains) a complete solution is found. The method used in this paper proved accurate for obtaining exact results on the value of the decay parameter. An example extending results of Miller [8] and Teugels [9] illustrates the procedure.

Keywords

DERIVED MARKOV CHAINSTRANSITION PROBABILITIESGEOMETRIC AND EXPONENTIAL DECAYSUBORDINATED STOCHASTIC PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 388 - 393
Copyright
Copyright © Applied Probability Trust 1974 

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References

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