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

2017 ◽  
Vol 17 (02) ◽  
pp. 1750015
Author(s):  
Lingtao Kong ◽  
Hongshuai Dai
Keyword(s):  
Complete Convergence ◽  
Convergence Rates ◽  
Complete Moment Convergence ◽  
Precise Asymptotics ◽  
Moment Convergence ◽  
Special Case

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

scholarly journals Second-Order Moment Convergence Rates for Spectral Statistics of Random Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Junshan Xie
Keyword(s):  
Random Matrices ◽  
Complete Convergence ◽  
Convergence Rates ◽  
Covariance Matrices ◽  
Second Order ◽  
Order Moment ◽  
Precise Asymptotics ◽  
Moment Convergence ◽  
Sample Covariance ◽  
Spectral Statistics

This paper considers the precise asymptotics of the spectral statistics of random matrices. Following the ideas of Gut and Spătaru (2000) and Liu and Lin (2006) on the precise asymptotics of i.i.d. random variables in the context of the complete convergence and the second-order moment convergence, respectively, we will establish the precise second-order moment convergence rates of a type of series constructed by the spectral statistics of Wigner matrices or sample covariance matrices.

scholarly journals Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1093-1104
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables

This paper we study and establish the complete convergence and complete moment convergence theorems under a sub-linear expectation space. As applications, the complete convergence and complete moment convergence for negatively dependent random variables with CV (exp (ln? |X|)) < ?, ? > 1 have been generalized to the sub-linear expectation space context. We extend some complete convergence and complete moment convergence theorems for the traditional probability space to the sub-linear expectation space. Our results generalize corresponding results obtained by Gut and Stadtm?ller (2011), Qiu and Chen (2014) and Wu and Jiang (2016). There is no report on the complete moment convergence under sub-linear expectation, and we provide the method to study this subject.

scholarly journals Precise Asymptotics for Complete Integral Convergence under Sublinear Expectations

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Complete Moment Convergence ◽  
Precise Asymptotics ◽  
Convergence Theorems ◽  
Sublinear Expectation ◽  
Moment Convergence

The aim of this paper is to study and establish the precise asymptotics for complete integral convergence theorems under a sublinear expectation space. As applications, the precise asymptotics for p0≤p≤2 order complete integral convergence theorems have been generalized to the sublinear expectation space context. We extend some precise asymptotics for complete moment convergence theorems from the traditional probability space to the sublinear expectation space. Our results generalize corresponding results obtained by Liu and Lin (2006). There is no report on the precise asymptotics under sublinear expectation, and we provide the method to study this subject.

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