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Bartlett spectrum and mixing properties of infinitely divisible random measures

Part of:Ergodic theoryStochastic processesDistribution theory - Probability

Published online by Cambridge University Press:  01 July 2016

Emmanuel Roy
Emmanuel Roy*
Affiliation:
Université Paris 13
*
∗ Current address: Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 13, UMR 7539, 99 avenue J. B. Clément, F-93430 Villetaneuse, France. Email address: roy@math.univ-paris13.fr
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Abstract

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We prove that the Bartlett spectrum of a stationary, infinitely divisible (ID) random measure determines ergodicity, weak mixing, and mixing. In this context, the Bartlett spectrum plays the same role as the spectral measure of a stationary Gaussian process.

Keywords

Infinitely divisible random measureinfinitely divisible point processCox processBartlett spectrumergodic theory

MSC classification

Primary:60G57: Random measures60G55: Point processes
Secondary:37A05: Measure-preserving transformations60E07: Infinitely divisible distributions; stable distributions

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 39 , Issue 4 , December 2007, pp. 893 - 897
Copyright
Copyright © Applied Probability Trust 2007 

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