Laws of large numbers and complete convergence for WOD random variables and their applications

2020 ◽  
pp. 1-26
Author(s):  
Chi Yao ◽  
Yongping He ◽  
Rui Wang ◽  
Xuejun Wang
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Laws Of Large Numbers ◽  
Large Numbers

scholarly journals COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF AANA RANDOM VARIABLES

2008 ◽  
Vol 50 (3) ◽  
pp. 351-357 ◽  
Author(s):  
GUANG-HUI CAI ◽  
BAO-CAI GUO
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Rocky Mountain ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

AbstractLet Xn, n ≥ 1 be an asymptotically almost negatively associated (AANA) sequence of random variables. Some complete convergence and Marcinkiewicz–Zygmund type strong laws of large numbers for an AANA sequence of random variables are obtained. The results obtained generalize the results of Kim, Ko and Lee (Kim, T. S., Ko, M. H. and Lee, I. H. 2004. On the strong laws for asymptotically almost negatively associated random variables. Rocky Mountain J. of Math. 34, 979–989.).

scholarly journals On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Aiting Shen ◽  
Ying Zhang ◽  
Andrei Volodin
Keyword(s):  
Strong Convergence ◽  
Mild Condition ◽  
Complete Convergence ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Independent And Identically Distributed

Letan,n≥1be a sequence of positive constants withan/n↑and letX,Xn,n≥1be a sequence of pairwise negatively quadrant dependent random variables. The complete convergence for pairwise negatively quadrant dependent random variables is studied under mild condition. In addition, the strong laws of large numbers for identically distributed pairwise negatively quadrant dependent random variables are established, which are equivalent to the mild condition∑n=1∞PX>an<∞. Our results obtained in the paper generalize the corresponding ones for pairwise independent and identically distributed random variables.

Laws of large numbers for q-dependent random variables and nonextensive statistical mechanics

2017 ◽  
Vol 31 (15) ◽  
pp. 1750117
Author(s):  
Marco A. S. Trindade
Keyword(s):  
Statistical Mechanics ◽  
Stochastic Processes ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Nonextensive Statistical Mechanics ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers

In this work, we prove a weak law and a strong law of large numbers through the concept of [Formula: see text]-product for dependent random variables, in the context of nonextensive statistical mechanics. Applications for the consistency of estimators are presented and connections with stochastic processes are discussed.

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