English

On Mukhin's necessary and sufficient condition for the validity of the local limit theorem

Probability 2024-07-09 v1

Abstract

Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition, with a significantly different formulation. This is the object of this short Note.

Keywords

Cite

@article{arxiv.2209.07968,
  title  = {On Mukhin's necessary and sufficient condition for the validity of the local limit theorem},
  author = {Michel J. G. Weber},
  journal= {arXiv preprint arXiv:2209.07968},
  year   = {2024}
}

Comments

4 pages. arXiv admin note: substantial text overlap with arXiv:2208.02700