1. 2021, Kolmogoroff’s Strong Law of Large Numbers holds for pairwise uncorrelated random variables

Title: Kolmogoroff’s Strong Law of Large Numbers holds for pairwise uncorrelated random variables.

Year: 2021.

Authors: Maximilian Janisch.

Abstract: Using the approach of N. Etemadi for the Strong Law of Large Numbers (SLLN) from 1981 and the elaboration of this approach by S. Csörgő, K. Tandori and V. Totik from 1983, I give weak conditions under which the SLLN still holds for pairwise uncorrelated (and also “quasi uncorrelated”) random variables. I am focusing in particular on random variables which are not identically distributed. The approach also delivers a simple proof for the classical SLLN.

Journal Reference: Theory of Probability and its Applications, 2021, Volume 66, Issue 2, Pages 263-275 (English); Teoriya Veroyatnostei i ee Primeneniya (Theory of Probability and its Applications), 2021, Volume 66, Issue 2, Pages 327-341 (Russian abstract). https://doi.org/10.4213/tvp5459

Available at arXiv: https://arxiv.org/abs/2005.03967.