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Limit theory for some positive stationary processes with infinite mean

Jon Aaronson, Roland Zweimüller (2014)

Annales de l'I.H.P. Probabilités et statistiques

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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