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

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.

arXiv comment4 pages. arXiv admin note: substantial text overlap with arXiv:2208.02700