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The existence of moments for stationary Markov chains

Published online by Cambridge University Press:  14 July 2016

R. L. Tweedie
R. L. Tweedie*
Affiliation:
Siromath, Sydney
*
∗ Postal address: SIROMATH Pty Ltd, 71 York Street, Sydney, NSW 2000, Australia.
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Abstract

We give conditions under which the stationary distribution π of a Markov chain admits moments of the general form ∫ f(x)π(dx), where f is a general function; specific examples include f(x) = xr and f(x) = esx. In general the time-dependent moments of the chain then converge to the stationary moments. We show that in special cases this convergence of moments occurs at a geometric rate. The results are applied to random walk on [0, ∞).

Keywords

INVARIANT MEASUREGEOMETRIC ERGODICITYMOMENT-GENERATING FUNCTIONHARRIS CHAIN
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 191 - 196
Copyright
Copyright © Applied Probability Trust 1983 

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References

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