Electronic Communications in Probability

An Erdős–Rényi law for nonconventional sums

Yuri Kifer

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 83, 8 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465321010

Digital Object Identifier
doi:10.1214/ECP.v20-4613

Mathematical Reviews number (MathSciNet)
MR3434200

Zentralblatt MATH identifier
1329.60065

Subjects
Primary: 60F15: Strong theorems
Secondary: 60F10: Large deviations

Keywords
laws of large numbers large deviations nonconventional sums

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Kifer, Yuri. An Erdős–Rényi law for nonconventional sums. Electron. Commun. Probab. 20 (2015), paper no. 83, 8 pp. doi:10.1214/ECP.v20-4613. https://projecteuclid.org/euclid.ecp/1465321010


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References

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