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Mixing properties of harris chains and autoregressive processes

Published online by Cambridge University Press:  24 August 2016

Krishna B. Athreya  and
Sastry G. Pantula
Krishna B. Athreya*
Affiliation:
Iowa State University
Sastry G. Pantula*
Affiliation:
North Carolina State University
*
∗Postal address: Statistical Laboratory, Snedecor Hall, Iowa State University, Ames, IA 50011, USA.
∗∗Postal address: Department of Statistics, North Carolina State University, School of Mathematical Sciences, Box 8203, Raleigh, NC 27695–8203, USA.
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Abstract

Let {Yn: n ≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn} is strong mixing, provided there exists a stationary probability distribution π (·) for {Yn}. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.

Keywords

STRONG AND UNIFORM MIXINGAUTOREGRESSIVE MOVING-AVERAGE PROCESSESHARRIS-RECURRENT CHAINS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 880 - 892
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research supported in part by NSF grant DMS-8502311.

References

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