Chung-Type Strong Laws and Almost Complete Convergence for Arrays of Measurable Operators

2021 ◽  
Author(s):  
Do The Son ◽  
Duong Xuan Giap ◽  
Nguyen Van Quang
Keyword(s):  
Complete Convergence ◽  
Strong Laws ◽  
Measurable Operators

scholarly journals On strong laws of large numbers for arrays of rowwise independent random elements

1993 ◽  
Vol 16 (3) ◽  
pp. 587-591 ◽  
Author(s):  
Abolghassem Bozorgnia ◽  
Ronald Frank Patterson ◽  
Robert Lee Taylor
Keyword(s):  
Banach Space ◽  
Density Estimation ◽  
Separable Banach Space ◽  
Complete Convergence ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Rowwise Independent

Let{Xnk}be an array of rowwise independent random elements in a separable Banach space of typer,1≤r≤2. Complete convergence ofn1/p∑k=1nXnkto0,0<p<r≤2is obtained whensup1≤k≤nE ‖Xnk‖v=O(nα),α≥0withv(1p−1r)>α+1. An application to density estimation is also given.

scholarly journals Complete convergence for arrays of minimal order statistics

2004 ◽  
Vol 2004 (44) ◽  
pp. 2325-2329 ◽  
Author(s):  
André Adler
Keyword(s):  
Order Statistics ◽  
Complete Convergence ◽  
Random Variables ◽  
Partial Sums ◽  
Minimal Order ◽  
Strong Laws ◽  
First Moment

For arrays of independent Pareto random variables, this paper establishes complete convergence for weighted partial sums for the smaller order statistics within each row. This result improves on past strong laws. Moreover, it shows that we can obtain a finite nonzero limit for our normalized partial sums under complete convergence even though the first moment of our order statistics is infinite.

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.

Sign in / Sign up

Export Citation Format

Share Document