Coboundaries in L ∞0

Dalibor Volný; Benjamin Weiss

doi:10.1016/j.anihpb.2004.01.004

Coboundaries in L ∞₀

Dalibor Volný^*
, Benjamin Weiss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let T be an ergodic automorphism of a probability space, f a bounded measurable function, S_n(f) = ∑_k=0^n-1 f ○ T^k. It is shown that the property that the probabilities μ( S_n(f) > n) are of order n^-p roughly corresponds to the existence of an approximation in L ∞ of f by functions (coboundaries) g - g ○ T, g ∈ L^p. Similarly, the probabilities μ( S_n(f) > n) are exponentially small iff f can be approximated by coboundaries g - g ○ T where g have finite exponential moments.

Original language	English
Pages (from-to)	771-778
Number of pages	8
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	40
Issue number	6
DOIs	https://doi.org/10.1016/j.anihpb.2004.01.004
State	Published - Nov 2004

Keywords

Coboundary
Probabilities of large deviations

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10.1016/j.anihpb.2004.01.004

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title = "Coboundaries in L ∞0",

abstract = "Let T be an ergodic automorphism of a probability space, f a bounded measurable function, Sn(f) = ∑k=0n-1 f ○ Tk. It is shown that the property that the probabilities μ( Sn(f) > n) are of order n-p roughly corresponds to the existence of an approximation in L ∞ of f by functions (coboundaries) g - g ○ T, g ∈ Lp. Similarly, the probabilities μ( Sn(f) > n) are exponentially small iff f can be approximated by coboundaries g - g ○ T where g have finite exponential moments.",

keywords = "Coboundary, Probabilities of large deviations",

author = "Dalibor Voln{\'y} and Benjamin Weiss",

year = "2004",

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doi = "10.1016/j.anihpb.2004.01.004",

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T1 - Coboundaries in L ∞0

AU - Volný, Dalibor

AU - Weiss, Benjamin

PY - 2004/11

Y1 - 2004/11

N2 - Let T be an ergodic automorphism of a probability space, f a bounded measurable function, Sn(f) = ∑k=0n-1 f ○ Tk. It is shown that the property that the probabilities μ( Sn(f) > n) are of order n-p roughly corresponds to the existence of an approximation in L ∞ of f by functions (coboundaries) g - g ○ T, g ∈ Lp. Similarly, the probabilities μ( Sn(f) > n) are exponentially small iff f can be approximated by coboundaries g - g ○ T where g have finite exponential moments.

AB - Let T be an ergodic automorphism of a probability space, f a bounded measurable function, Sn(f) = ∑k=0n-1 f ○ Tk. It is shown that the property that the probabilities μ( Sn(f) > n) are of order n-p roughly corresponds to the existence of an approximation in L ∞ of f by functions (coboundaries) g - g ○ T, g ∈ Lp. Similarly, the probabilities μ( Sn(f) > n) are exponentially small iff f can be approximated by coboundaries g - g ○ T where g have finite exponential moments.

KW - Coboundary

KW - Probabilities of large deviations

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SN - 0246-0203

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 6

ER -

Coboundaries in L ∞₀

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Keywords

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