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Mixing of cluster point processes

Published online by Cambridge University Press:  14 July 2016

G. M. Laslett
G. M. Laslett*
Affiliation:
CSIRO Division of Mathematics and Statistics, South Melbourne
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Abstract

This paper deals with the preservation of strong forms of mixing of point processes under the clustering operation. Strong, ϕ -, and *-mixing possess an increasing degree of uniformity of their asymptotic independence, and this turns out to be a significant factor in their preservation. In particular, it is indicated that ϕ-mixing may be maintained only under very stringent conditions (bounded clusters), whereas strong mixing is maintained under considerably milder conditions.

Keywords

POINT PROCESSCLUSTER PROCESSMIXING

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 4 , December 1978, pp. 715 - 725
Copyright
Copyright © Applied Probability Trust 1978 

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