On the speed of convergence in the local limit theorem for triangular arrays of random variables

TL;DR

This paper investigates how quickly the distribution of sums of triangular array random variables approaches the limit density described by the local limit theorem, providing an upper bound on the convergence speed.

Contribution

It establishes an upper bound on the convergence speed to the limit density in the local limit theorem for triangular arrays of random variables.

Findings

Derived an explicit upper bound for convergence speed

Applicable to a broad class of triangular arrays

Enhances understanding of limit theorem convergence rates

Abstract

We establish the upper bound on the speed of convergence to the infinitely divisible limit density in the local limit theorem for triangular arrays of random variables $\{X_{k,n},\, k=1,..,a_n, \, n\in \nat\}$.