Limit theory for some positive stationary processes with infinite mean

Jon Aaronson; Roland Zweimüller

doi:10.1214/12-AIHP513

Limit theory for some positive stationary processes with infinite mean

Jon Aaronson, Roland Zweimüller

School of Mathematical Sciences

University of Vienna

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	256-284
Number of pages	29
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	50
Issue number	1
DOIs	https://doi.org/10.1214/12-AIHP513
State	Published - Feb 2014

Keywords

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

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AB - 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.

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KW - Mixing coefficient

KW - One-sided law of iterated logarithm

KW - Pointwise dual ergodic

KW - Stable limit

KW - Transfer operator

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Limit theory for some positive stationary processes with infinite mean

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Keywords

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