Limit theory for some positive stationary processes with infinite mean

Jon Aaronson, Roland Zweimüller

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)256-284
Number of pages29
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number1
StatePublished - Feb 2014


  • 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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