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2015 An Erdős–Rényi law for nonconventional sums
Yuri Kifer
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Electron. Commun. Probab. 20: 1-8 (2015). DOI: 10.1214/ECP.v20-4613


We obtain the Erdős–Rényi type law of large numbers for "nonconventional" sums of the form $S_n=\sum_{m=1}^nF(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of i.i.d. random variables and $F$ is a bounded Borel function. The proof relies on nonconventional large deviations obtained in a previous work.


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Yuri Kifer. "An Erdős–Rényi law for nonconventional sums." Electron. Commun. Probab. 20 1 - 8, 2015.


Accepted: 7 November 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60065
MathSciNet: MR3434200
Digital Object Identifier: 10.1214/ECP.v20-4613

Primary: 60F15
Secondary: 60F10

Keywords: large deviations , laws of large numbers , nonconventional sums

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