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arXiv · 1801.09265

The weakly dependent strong law of large numbers revisited

Abdelmalek Abdesselam
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Abstract

We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of convergence. Our proof does not use maximal inequalities and is instead inspired by the method of multiscale large versus small field decompositions in constructive quantum field theory.

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Abdelmalek Abdesselam. 2018-01-28. The weakly dependent strong law of large numbers revisited. https://arxiv.org/abs/1801.09265

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