On strong law of large numbers for non identically distributed random variables

I. V. Kozlov; A. Yu. Veretennikov

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arXiv · 2506.07508

On strong law of large numbers for non identically distributed random variables

I. V. Kozlov·A. Yu. Veretennikov

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Abstract

A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of the expectation for each summand: the members of an ``infrequent'' part of the whole sequence may have moments of orders converging to zero.

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I. V. Kozlov, A. Yu. Veretennikov. 2025-06-09. On strong law of large numbers for non identically distributed random variables. https://arxiv.org/abs/2506.07508

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