Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Limit theory for some positive stationary processes with infinite mean

Jon Aaronson and Roland Zweimüller

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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.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 50, Number 1 (2014), 256-284.

First available in Project Euclid: 1 January 2014

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Zentralblatt MATH identifier

Primary: 60Fxx: Limit theorems [See also 28Dxx, 60B12]
Secondary: 37A40: Nonsingular (and infinite-measure preserving) transformations 60G10: Stationary processes

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


Aaronson, Jon; Zweimüller, Roland. Limit theory for some positive stationary processes with infinite mean. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 1, 256--284. doi:10.1214/12-AIHP513.

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