Open Access
February 2014 Limit theory for some positive stationary processes with infinite mean
Jon Aaronson, Roland Zweimüller
Ann. Inst. H. Poincaré Probab. Statist. 50(1): 256-284 (February 2014). DOI: 10.1214/12-AIHP513

Abstract

We prove stable limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from nonintegrable observables over certain piecewise expanding maps. This is done by extending Darling–Kac theory to a suitable family of infinite measure preserving transformations.

Nous prouvons des théorèmes limites et des lois du logarithme itéré unilatérales pour une classe de processus stochastiques positifs, mélangeants et stationnaires. Cette classe contient en particulier les processus obtenus par des observables nonintégrables de certaines applications dilatantes. Ceci est obtenu en généralisant la théorie de Darling–Kac à une famille appropriée de transformations préservant la mesure.

Citation

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Jon Aaronson. Roland Zweimüller. "Limit theory for some positive stationary processes with infinite mean." Ann. Inst. H. Poincaré Probab. Statist. 50 (1) 256 - 284, February 2014. https://doi.org/10.1214/12-AIHP513

Information

Published: February 2014
First available in Project Euclid: 1 January 2014

zbMATH: 1291.60067
MathSciNet: MR3161531
Digital Object Identifier: 10.1214/12-AIHP513

Subjects:
Primary: 60Fxx
Secondary: 37A40 , 60G10

Keywords: Darling–Kac theorem , Infinite ergodic theory , Infinite invariant measure , Mixing coefficient , One-sided law of iterated logarithm , Pointwise dual ergodic , Stable limit , Transfer operator

Rights: Copyright © 2014 Institut Henri Poincaré

Vol.50 • No. 1 • February 2014
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