An Erd\" os-R\' enyi law for nonconventional sums

Yuri Kifer

An Erd\" os-R\' enyi law for nonconventional sums

Probability 2016-04-05 v2

Authors: Yuri Kifer

Abstract

We obtain rge Erd\" os-R\' enyi type law of large numbers for "nonconventional" sums of the form $S_n=\sum^n_{m=1}F(X_m,X_{2m},...,X_{\ell m})$ 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 [8].

Keywords

nonconventional sums Erdős-Rényi law law of large numbers large deviations i.i.d. random variables Borel function

Cite

@article{arxiv.1510.02236,
  title  = {An Erd\" os-R\' enyi law for nonconventional sums},
  author = {Yuri Kifer},
  journal= {arXiv preprint arXiv:1510.02236},
  year   = {2016}
}

Related papers

View all related →