Displaying similar documents to “Random ergodic theorems with universally representative sequences”

On the distribution function of the majorant of ergodic means

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 f * = s u p N 1 / N ∑ m = 0 N - 1 f ∘ T m . In this paper we mainly investigate the question of whether (i) ʃ a ∞ | μ ( f * > t ) - 1 / t ʃ ( f * > t ) f d μ | d t < ∞ and whether (ii) ʃ a ∞ | μ ( f * > t ) - 1 / t ʃ ( f > t ) f d μ | d t < ∞ 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 f ∘ T m are independent. Related inequalities are proved. Some examples and counterexamples are constructed. Several known results are obtained as corollaries. ...

Large deviations for generic stationary processes

Emmanuel Lesigne, Dalibor Volný (2000)

Colloquium Mathematicae

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Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.

Remarks on the tightness of cocycles

Jon Aaronson, Benjamin Weiss (2000)

Colloquium Mathematicae

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We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.