arXiv:2209.07968 Abstract | arXiv Analytics

arXiv:2209.07968 [math.PR]Abstract References Reviews Resources

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

Published 2022-09-16Version 1

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.

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

Categories: math.PR

Subjects: 60F15, 60G50, 60F05

Keywords: local limit theorem, sufficient condition, mukhins necessary, weaker necessary, succint proof

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