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.
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}, pages = {256--284}, publisher = {Gauthier-Villars}, volume = {50}, number = {1}, year = {2014}, doi = {10.1214/12-AIHP513}, mrnumber = {3161531}, zbl = {1291.60067}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/12-AIHP513/} }
TY - JOUR AU - Aaronson, Jon AU - Zweimüller, Roland TI - Limit theory for some positive stationary processes with infinite mean JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2014 SP - 256 EP - 284 VL - 50 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/12-AIHP513/ DO - 10.1214/12-AIHP513 LA - en ID - AIHPB_2014__50_1_256_0 ER -
%0 Journal Article %A Aaronson, Jon %A Zweimüller, Roland %T Limit theory for some positive stationary processes with infinite mean %J Annales de l'I.H.P. Probabilités et statistiques %D 2014 %P 256-284 %V 50 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/12-AIHP513/ %R 10.1214/12-AIHP513 %G en %F 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://archive.numdam.org/articles/10.1214/12-AIHP513/
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