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On strong mixing and Leadbetter's D condition

Published online by Cambridge University Press:  14 July 2016

Michael R. Chernick
Michael R. Chernick*
Affiliation:
The Aerospace Corporation
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Abstract

Strong mixing is a condition which is often assumed to prove limit theorems for strictly stationary processes. Leadbetter's condition D(un) is used to prove limit theorems for maxima of stationary processes.

A sufficient condition for strong mixing to hold is given for the case where the process satisfies a pth-order Markov property. This condition can be easy to check for when p is small. This point is illustrated by two examples of first-order autoregressive processes.

The condition D(un) is shown to hold for any stationary Markov process.

Keywords

MARKOV PROCESSESPTH-ORDER MARKOV PROPERTYAUTOREGRESSIVE PROCESSESSTRONG MIXING CONDITIONDISTRIBUTIONAL MIXING CONDITIONASYMPTOTIC DISTRIBUTION THEORYSTRICTLY STATIONARY PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 764 - 769
Copyright
Copyright © Applied Probability Trust 

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