Rate of convergence to alpha stable law using Zolotarev distance : technical report

TL;DR

This paper investigates the rate at which sums of i.i.d. random variables converge to an alpha-stable law using Zolotarev distance, providing bounds for 1 < alpha < 2 in the generalized CLT without requiring finite variance.

Contribution

It introduces a method to quantify the convergence rate to alpha-stable laws using Zolotarev distance, extending the classical CLT to non-square integrable cases.

Findings

Provides explicit convergence rate bounds for 1 < alpha < 2

Extends CLT results to heavy-tailed distributions

Utilizes Zolotarev distance for precise convergence measurement

Abstract

This paper considers the question of the rate of convergence to ${\alpha}$- stable laws, using arguments based on the Zolotarev distance to prove bounds. We provide a rate of convergence to ${\alpha}$-stable random variable where 1 < ${\alpha}$ < 2, in the generalized CLT, that is, for the partial sums of independent identically distributed random variables which are not assumed to be square integrable. This work is a technical report based on the Zolotarev paper in [1].