A remark on Denjoy's inequality and Herman's theorem
Lennart Carleson (1979)
Publications Mathématiques de l'IHÉS
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Lennart Carleson (1979)
Publications Mathématiques de l'IHÉS
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Antonis Bisbas (1996)
Colloquium Mathematicae
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Peter Raith (1989)
Studia Mathematica
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Kalpazidou, Sofia, Knopfmacher, Arnold, Knopfmacher, John (1991)
Portugaliae mathematica
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Lasha Epremidze (1992)
Studia Mathematica
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Let T be a measure-preserving ergodic transformation of a measure space (X,,μ) and, for f ∈ L(X), let . In this paper we mainly investigate the question of whether (i) and whether (ii) for some a > 0. It is proved that (i) holds for every f ≥ 0. (ii) holds if f ≥ 0 and f log log (f + 3) ∈ L(X) or if μ(X) = 1 and the random variables are independent. Related inequalities are proved. Some examples and counterexamples are constructed. Several known results are obtained as corollaries. ...
Roger J. Metzger (2000)
Annales de l'I.H.P. Analyse non linéaire
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Firas Rassoul-Agha, Timo Seppäläinen (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative entropy.