# Local limit theorems for smoothed Bernoulli and other convolutions

## TL;DR

This paper investigates the asymptotic behavior of the densities of sums of independent random variables convolved with small continuous noise, providing insights into their local limit theorems.

## Contribution

It introduces new local limit theorems for smoothed Bernoulli and other convolutions, extending classical results to include small noise perturbations.

## Key findings

- Derived asymptotic density behaviors for smoothed Bernoulli sums
- Extended local limit theorems to convolutions with small continuous noise
- Provided conditions under which classical limit theorems hold in the smoothed setting

## Abstract

We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.