Convergence rates in precise asymptotics for a kind of complete moment convergence

TL;DR

This paper investigates the convergence rates in precise asymptotics for a generalized form of complete moment convergence, extending previous work on complete convergence and providing new insights into its convergence behavior.

Contribution

It introduces the study of convergence rates in precise asymptotics for a generalized complete moment convergence, expanding understanding beyond traditional complete convergence.

Findings

Derived explicit convergence rates for the generalized complete moment convergence

Extended existing theories on complete convergence to a broader class of convergence

Provided mathematical bounds and asymptotic behaviors for the convergence rates

Abstract

In Liu and Lin (Statist. Probab. Letters, 2006), they introduced a kind of complete moment convergence which includes complete convergence as a special case. Inspired by the study of complete convergence, in this paper, we study the convergence rates of the precise asymptotics for this kind of complete moment convergence and get the corresponding convergence rates.