Limit theory for some positive stationary processes with infinite mean

Aaronson, Jon; Zweimüller, Roland

Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 1, pp. 256-284.

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.

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.

Classification : 60Fxx, 37A40, 60G10
Mots clés : infinite invariant measure, transfer operator, infinite ergodic theory, Darling-Kac theorem, pointwise dual ergodic, mixing coefficient, stable limit, one-sided law of iterated logarithm

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