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Energy of Markov chains

Published online by Cambridge University Press:  01 July 2016

R. Syski
R. Syski*
Affiliation:
University of Maryland
*
∗ Postal address: Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A.
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Abstract

After preliminaries on Markov chains, supermartingales and potential theory (Section 1), the energy of a potential supermartingale generated by an increasing process is defined. The paper examines some properties of the energy of potentials of the form U t = p(X t ) where p is a purely excessive function (which is also a potential of a charge) for a Markov chain (X t ). Also, the mutual energy of two potentials associated with the same Markov chain is discussed. Finally, several applications and examples are worked out in detail (Section 3).

Keywords

BALAYAGEENERGYEXCESSIVE FUNCTIONSINCREASING PROCESSMARKOV CHAINPOTENTIALSSUPERMARTINGALES

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 3 , September 1979, pp. 542 - 575
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

This paper is an expanded version of one presented at the Fourth Conference on Stochastic processs and their Applications, York University, Ontario, Canada, in August 1974.

References

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