A Note on Complete Convergence for Arrays of Rowwise Independent Banach Space Valued Random Elements

2010 ◽  
Vol 28 (3) ◽  
pp. 565-575 ◽  
Author(s):  
Pingyan Chen ◽  
Víctor Hernández ◽  
Henar Urmeneta ◽  
Andrei Volodin
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Random Elements ◽  
Rowwise Independent

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

1987 ◽  
Vol 10 (4) ◽  
pp. 805-814 ◽  
Author(s):  
Robert Lee Taylor ◽  
Tien-Chung Hu
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Complete Convergence ◽  
Almost Sure Convergence ◽  
Random Variable ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Random Elements ◽  
Rowwise Independent ◽  
Uniformly Bounded

Let{Xnk}be an array of rowwise independent random elements in a separable Banach space of typep+δwithEXnk=0for allk,n. The complete convergence (and hence almost sure convergence) ofn−1/p∑k=1nXnk to 0,1≤p<2, is obtained when{Xnk}are uniformly bounded by a random variableXwithE|X|2p<∞. When the array{Xnk}consists of i.i.d, random elements, then it is shown thatn−1/p∑k=1nXnkconverges completely to0if and only ifE‖X11‖2p<∞.

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 sums of arrays of random elements

2000 ◽  
Vol 23 (11) ◽  
pp. 789-794 ◽  
Author(s):  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Moment Conditions ◽  
Random Elements ◽  
Rowwise Independent

Let{Xni}be an array of rowwise independentB-valued random elements and{an}constants such that0<an↑∞. Under some moment conditions for the array, it is shown that∑i=1nXni/anconverges to0completely if and only if∑i=1nXni/anconverges to0in probability.

On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements

2002 ◽  
Vol 47 (3) ◽  
pp. 533-547 ◽  
Author(s):  
Tien-Chung Hu ◽  
Tien-Chung Hu ◽  
Deli Li ◽  
Deli Li ◽  
Andrew Rosalsky ◽  
...  
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Weighted Sums ◽  
Random Elements

On the Rate of Complete Convergence for Weighted Sums of Arrays of Banach Space Valued Random Elements

2003 ◽  
Vol 47 (3) ◽  
pp. 455-468 ◽  
Author(s):  
T. C. Hu ◽  
D. Li ◽  
A. Rosalsky ◽  
A. I. Volodin
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Weighted Sums ◽  
Random Elements

scholarly journals ON COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM ELEMENTS

2007 ◽  
Vol 44 (2) ◽  
pp. 467-476 ◽  
Author(s):  
Soo-Hak Sung ◽  
Manuel Ordonez Cabrera ◽  
Tien-Chung Hu
Keyword(s):  
Complete Convergence ◽  
Random Elements ◽  
Rowwise Independent

scholarly journals On complete convergence in a Banach space

1994 ◽  
Vol 17 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Anna Kuczmaszewska ◽  
Dominik Szynal
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Sufficient Conditions ◽  
Large Numbers ◽  
Random Elements

Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.

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