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An Erdős-Rényi law for nonconventional sums. (English) Zbl 1329.60065

Electron. Commun. Probab. 20, Paper No. 83, 8 p. (2015); erratum ibid. 21, Paper No. 33, 1 p. (2016).
Summary: We obtain the Erdős-Rényi type law of large numbers for “nonconventional” sums of the form \(S_n=\sum_{m=1}^nF(X_m,X_{2m},\dots,X_{\ell m})\) where \(X_1,X_2,\dots\) 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.

MSC:

60F15 Strong limit theorems
60F10 Large deviations
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