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arXiv · 1608.01851

Functional Erd\"os-R\'enyi law of large numbers for nonconventional sums under weak dependence

Yuri Kifer
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Abstract

We obtain a functional Erd\H os-R\' enyi law of large numbers for "nonconventional" sums of the form $\Sig_n=\sum_{m=1}^nF(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of exponentially fast $\psi$-mixing random vectors and $F$ is a Borel vector function extendin in several directions our previous result concerning i.i.d. random variables $X_1,X_2,...$.

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Yuri Kifer. 2016-08-05. Functional Erd\"os-R\'enyi law of large numbers for nonconventional sums under weak dependence. https://arxiv.org/abs/1608.01851

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