Limit theory for some positive stationary processes with infinite mean
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 1, p. 256-284

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.

DOI : https://doi.org/10.1214/12-AIHP513
Classification:  60Fxx,  37A40,  60G10
Keywords: infinite invariant measure, transfer operator, infinite ergodic theory, Darling-Kac theorem, pointwise dual ergodic, mixing coefficient, stable limit, one-sided law of iterated logarithm
@article{AIHPB_2014__50_1_256_0,
     author = {Aaronson, Jon and Zweim\"uller, Roland},
     title = {Limit theory for some positive stationary processes with infinite mean},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {1},
     year = {2014},
     pages = {256-284},
     doi = {10.1214/12-AIHP513},
     zbl = {1291.60067},
     mrnumber = {3161531},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_1_256_0}
}
Aaronson, Jon; Zweimüller, Roland. Limit theory for some positive stationary processes with infinite mean. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 1, pp. 256-284. doi : 10.1214/12-AIHP513. http://www.numdam.org/item/AIHPB_2014__50_1_256_0/

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