A Note on the Inverse Moments for Nonnegative -Mixing Random Variables

Aiting Shen

doi:10.1155/2011/185160

Abstract

Wu et al. (2009) studied the asymptotic approximation of inverse moments for nonnegative independent random variables. Shen et al. (2011) extended the result of Wu et al. (2009) to the case of -mixing random variables. In the paper, we will further study the asymptotic approximation of inverse moments for nonnegative -mixing random variables, which improves the corresponding results of Wu et al. (2009), Wang et al. (2010), and Shen et al. (2011) under the case of identical distribution.

Highlights

We will recall the definition of ρ-mixing random variables
Let {Xn, n ≥ 1} be a sequence of random variables defined on a fixed probability space
The main purpose of the paper is to study the asymptotic approximation of inverse moments for nonnegative ρ-mixing random variables with identical distribution

Summary

Aiting Shen

Wu et al 2009 studied the asymptotic approximation of inverse moments for nonnegative independent random variables. Shen et al 2011 extended the result of Wu et al 2009 to the case of ρ-mixing random variables. We will further study the asymptotic approximation of inverse moments for nonnegative ρ-mixing random variables, which improves the corresponding results of Wu et al 2009 , Wang et al 2010 , and Shen et al 2011 under the case of identical distribution

Introduction

EXn t n

Let n

Var Xn n