Integrability conditions on coboundary and transfer function for limit theorems

zbMATH Open1337.60041arXiv1505.05763MaRDI QIDQ2805289

Publication date: 11 May 2016

Published in: ALEA. Latin American Journal of Probability and Mathematical Statistics (Search for Journal in Brave)

Abstract: For a measure preserving automorphism

T

of a probability space, we provide conditions on the tail function of

g c o l o n O m e g a o m a t h b b R

and

g - g c i r c T

which guarantee limit theorems among the weak invariance principle, Marcinkievicz-Zygmund strong law of large numbers and the law of iterated logarithm to hold for

f : = m + g - g c i r c T

, where

(m c i r c T^{i})_{i g e q s l a n t 0}

is a martingale differences sequence.

Full work available at URL: https://arxiv.org/abs/1505.05763

zbMATH Keywords

martingales law of the iterated logarithm weak invariance principle coboundary strictly stationary processes Marcinkievicz-Zygmund strong law of large numbers

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

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