## Electronic Journal of Probability

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

Yuri Kifer

#### Abstract

We obtain a functional Erdős–Rényi law of large numbers for “nonconventional” sums of the form $\Sigma _n=\sum _{m=1}^n F(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of exponentially fast $\psi$-mixing random vectors and $F$ is a Borel vector function extending in several directions [18] where only i.i.d. random variables $X_1,X_2,...$ were considered.

#### Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 23, 17 pp.

Dates
Accepted: 16 February 2017
First available in Project Euclid: 1 March 2017

https://projecteuclid.org/euclid.ejp/1488337348

Digital Object Identifier
doi:10.1214/17-EJP39

Mathematical Reviews number (MathSciNet)
MR3622893

Zentralblatt MATH identifier
1359.60042

Subjects
Primary: 60F15: Strong theorems
Secondary: 60F10, 60F17, 37D20

#### Citation

Kifer, Yuri. Functional Erdős-Rényi law of large numbers for nonconventional sums under weak dependence. Electron. J. Probab. 22 (2017), paper no. 23, 17 pp. doi:10.1214/17-EJP39. https://projecteuclid.org/euclid.ejp/1488337348

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