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Moments for stationary and quasi-stationary distributions of markov chains

Published online by Cambridge University Press:  14 July 2016

E. Seneta  and
R. L. Tweedie
E. Seneta*
Affiliation:
University of Sydney
R. L. Tweedie*
Affiliation:
SIROMATH Pty Ltd
*
∗Postal address: Department of Mathematical Statistics, University of Sydney, Sydney, NSW 2006, Australia.
∗∗Postal address: SIROMATH Pty Ltd, 31 Market St, Sydney, NSW 2000, Australia.
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Abstract

A necessary and sufficient set of conditions is given for the finiteness of a general moment of the R -invariant measure of an R -recurrent substochastic matrix. The conditions are conceptually related to Foster's theorem. The result extends that of [8], and is illustratively applied to the single and multitype subcritical Galton–Watson process to find conditions for Yaglom-type conditional limit distributions to have finite moments.

Keywords

IRREDUCIBLE R-POSITIVE MATRIXR-INVARIANT MEASURETABOO STATESMOMENTSSUBCRITICAL BRANCHING PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 148 - 155
Copyright
Copyright © Applied Probability Trust 1985 

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References

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