A sufficient condition for local limit theorem

TL;DR

This paper provides a new sufficient condition for the local limit theorem using multiple convolutions of probability density functions, advancing theoretical understanding in probability theory.

Contribution

It introduces a novel sufficient condition for the local limit theorem based on infinite convolutions of density functions.

Findings

Established a new criterion for the local limit theorem

Utilized infinite convolutions of densities in the proof

Contributed to the theoretical foundation of probability limit theorems

Abstract

We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.