Limit theory for some positive stationary processes with infinite mean

作者：Aaronson Jon^*; Zweimueller Roland

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2014, 50(1): 256-284.

DOI：10.1214/12-AIHP513

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

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.

• 出版日期2014-2