Functional Erdős-Rényi law of large numbers for nonconventional sums under weak dependence

Yuri Kifer

doi:10.1214/17-EJP39

Functional Erdős-Rényi law of large numbers for nonconventional sums under weak dependence

Yuri Kifer^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

3 Scopus citations

Abstract

We obtain a functional Erdős–Rényi law of large numbers for “nonconventional” sums of the form Σ_n = ∑ⁿ_m=1 F(X_m, X_2m,…, X_ℓm) where X₁, X₂,… is a sequence of exponentially fast ψ-mixing random vectors and F is a Borel vector function extending in several directions [18] where only i.i.d. random variables X₁, X₂,… were considered.

Original language	English
Journal	Electronic Journal of Probability
Volume	22
DOIs	https://doi.org/10.1214/17-EJP39
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 University of Washington. All rights reserved.

Keywords

Hyperbolic diffeomorphisms
Large deviations
Laws of large numbers
Markov chains
Nonconventional sums

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10.1214/17-EJP39

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abstract = "We obtain a functional Erd{\H o}s–R{\'e}nyi law of large numbers for “nonconventional” sums of the form Σn = ∑nm=1 F(Xm, X2m,…, Xℓm) where X1, X2,… is a sequence of exponentially fast ψ-mixing random vectors and F is a Borel vector function extending in several directions [18] where only i.i.d. random variables X1, X2,… were considered.",

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AB - We obtain a functional Erdős–Rényi law of large numbers for “nonconventional” sums of the form Σn = ∑nm=1 F(Xm, X2m,…, Xℓm) where X1, X2,… is a sequence of exponentially fast ψ-mixing random vectors and F is a Borel vector function extending in several directions [18] where only i.i.d. random variables X1, X2,… were considered.

KW - Hyperbolic diffeomorphisms

KW - Large deviations

KW - Laws of large numbers

KW - Markov chains

KW - Nonconventional sums

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Functional Erdős-Rényi law of large numbers for nonconventional sums under weak dependence

Abstract

Bibliographical note

Keywords

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