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), p. 256-284 / Harvested from Numdam
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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.

Publié le : 2014-01-01
DOI : https://doi.org/10.1214/12-AIHP513
Classification:  60Fxx,  37A40,  60G10 
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     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},
     volume = {50},
     year = {2014},
     pages = {256-284},
     doi = {10.1214/12-AIHP513},
     mrnumber = {3161531},
     zbl = {1291.60067},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2014__50_1_256_0}
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Aaronson, Jon; Zweimüller, Roland. Limit theory for some positive stationary processes with infinite mean. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) pp. 256-284. doi : 10.1214/12-AIHP513. http://gdmltest.u-ga.fr/item/AIHPB_2014__50_1_256_0/

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