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

Probability 2025-06-10 v1

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.

Keywords

Cite

@article{arxiv.2506.07508,
  title  = {On strong law of large numbers for non identically distributed random variables},
  author = {I. V. Kozlov and A. Yu. Veretennikov},
  journal= {arXiv preprint arXiv:2506.07508},
  year   = {2025}
}

Comments

9 pages, 24 references