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Harmonic functions for a class of Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  09 April 2009

H. Cohn
H. Cohn
Affiliation:
Department of Statistics University of MelbourneParkville, Australia
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Abstract

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A class of Markov chains is considered for which a certain property of the tail events makes bounded harmonic functions obtainable from bounded space-time harmonic functions. Applications to almost surely convergent Markov chains are given and, in particular, a representation of Martin-Doob-Hunt type is derived for all bounded harmonic functions of a finite mean supercritical branching process.

MSC classification

Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 4 , December 1979 , pp. 413 - 422
Copyright
Copyright © Australian Mathematical Society 1979

References

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