On the strong law of large numbers and -convergence for double arrays of random elements in -uniformly smooth Banach spaces

2009 ◽  
Vol 79 (18) ◽  
pp. 1891-1899 ◽  
Author(s):  
Nguyen Van Quang ◽  
Nguyen Van Huan
Keyword(s):  
Banach Spaces ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Uniformly Smooth ◽  
Large Numbers ◽  
Random Elements ◽  
Uniformly Smooth Banach Spaces

scholarly journals Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements

2007 ◽  
Vol 2007 ◽  
pp. 1-15
Author(s):  
Kuo-Liang Su
Keyword(s):  
Banach Spaces ◽  
Law Of Large Numbers ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Random Elements

It will be shown and induced that thed-dimensional indices in the Banach spaces version conditions∑n(E‖Xn‖p/|nα|p)<∞are sufficient to yieldlimmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued random variables.

Marcinkiewicz-Zygmund type law of large numbers for double arrays of random elements in Banach spaces

2009 ◽  
Vol 30 (4) ◽  
pp. 337-346 ◽  
Author(s):  
Le Van Dung ◽  
Thuntida Ngamkham ◽  
Nguyen Duy Tien ◽  
A. I. Volodin
Keyword(s):  
Banach Spaces ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
Random Elements

A REMARK ON THE STRONG LAW FOR B-VALUED ARRAYS OF RANDOM ELEMENTS

2010 ◽  
Vol 82 (1) ◽  
pp. 31-43 ◽  
Author(s):  
TIEN-CHUNG HU ◽  
PING YAN CHEN ◽  
N. C. WEBER
Keyword(s):  
Law Of Large Numbers ◽  
Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Strong Law ◽  
Rate Law ◽  
Large Numbers ◽  
Random Elements

AbstractThe conditions in the strong law of large numbers given by Li et al. [‘A strong law for B-valued arrays’, Proc. Amer. Math. Soc.123 (1995), 3205–3212] for B-valued arrays are relaxed. Further, the compact logarithm rate law and the bounded logarithm rate law are discussed for the moving average process based on an array of random elements.

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