Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers

2009 ◽  
Vol 23 (1) ◽  
pp. 169-192 ◽  
Author(s):  
Guodong Xing ◽  
Shanchao Yang
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Rates Of Convergence ◽  
Exponential Inequalities ◽  
Strong Law ◽  
Associated Random Variables ◽  
Large Numbers

SOME LIMITING BEHAVIOR FOR ASYMPTOTICALLY NEGATIVE ASSOCIATED RANDOM VARIABLES

2016 ◽  
Vol 32 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Convergence Theorem ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Independent Random Variables ◽  
Strong Law ◽  
Limiting Behavior ◽  
Associated Random Variables ◽  
Large Numbers

In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.

scholarly journals Complete moment convergence for weighted sums of negatively orthant dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1195-1206 ◽  
Author(s):  
Xuejun Wang ◽  
Zhiyong Chen ◽  
Ru Xiao ◽  
Xiujuan Xie
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Strong Law ◽  
Associated Random Variables ◽  
Moment Convergence ◽  
Large Numbers

In this paper, the complete moment convergence and the integrability of the supremum for weighted sums of negatively orthant dependent (NOD, in short) random variables are presented. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for NODrandom variables are obtained. The results established in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.

scholarly journals On Complete Convergence of Weighted Sums for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Wenzhi Yang ◽  
Xinghui Wang
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Type Result ◽  
Strong Law ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

Let{Xni,i≥1,n≥1}be an array of rowwise asymptotically almost negatively associated (AANA, in short) random variables. The complete convergence for weighted sums of arrays of rowwise AANA random variables is studied, which complements and improves the corresponding result of Baek et al. (2008). As applications, the Baum and Katz type result for arrays of rowwise AANA random variables and the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of AANA random variables are obtained.

scholarly journals Strong and Weak Convergence for Asymptotically Almost Negatively Associated Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Aiting Shen ◽  
Ranchao Wu
Keyword(s):  
Weak Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong And Weak Convergence ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated ◽  
Independent And Identically Distributed

The strong law of large numbers for sequences of asymptotically almost negatively associated (AANA, in short) random variables is obtained, which generalizes and improves the corresponding one of Bai and Cheng (2000) for independent and identically distributed random variables to the case of AANA random variables. In addition, the Feller-type weak law of large number for sequences of AANA random variables is obtained, which generalizes the corresponding one of Feller (1946) for independent and identically distributed random variables.

scholarly journals Exponential inequalities under sub-linear expectations with applications to strong law of large numbers

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 2951-2961
Author(s):  
Xufei Tang ◽  
Xuejun Wang ◽  
Yi Wu
Keyword(s):  
Convergence Rate ◽  
Strong Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Exponential Inequalities ◽  
Strong Law ◽  
Large Numbers ◽  
Strong Convergence Rate

In this paper, we give some exponential inequalities for extended independent random variables under sub-linear expectations. As an application, we obtain the strong convergence rate O(n-1/2 ln1/2 n) for the strong law of large numbers under sub-linear expectations, which generalizes some corresponding ones under the classical linear expectations.

Obtaining Prescribed Rates of Convergence for the Ergodic Theorem

1983 ◽  
Vol 35 (6) ◽  
pp. 1129-1146 ◽  
Author(s):  
G. L. O'Brien
Keyword(s):  
Ergodic Theorem ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Rates Of Convergence ◽  
Stationary Sequence ◽  
Strong Law ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
The Law ◽  
Image Position

Let {Yn, n ∊ Z} be an ergodic strictly stationary sequence of random variables with mean zero, where Z denotes the set of integers. For n ∊ N = {1, 2, …}, let Sn = Y1 + Y2 + … + Yn. The ergodic theorem, alias the strong law of large numbers, says that n–lSn → 0 as n → ∞ a.s. If the Yn's are independent and have variance one, the law of the iterated logarithm tells us that this convergence takes place at the rate in the sense that1It is our purpose here to investigate what other rates of convergence are possible for the ergodic theorem, that is to say, what sequences {bn, n ≧ 1} have the property that2for some ergodic stationary sequence {Yn, n ∊ Z}.

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