Convergence rates in the law of large numbers for arrays of Banach space valued random elements

2005 ◽  
Vol 72 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Tibor Tómács
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Convergence Rates ◽  
Large Numbers ◽  
Random Elements ◽  
The Law

scholarly journals Convergence rates in the law of large numbers for Banach-valued dependent variables

10.4213/tvp78 ◽  
2007 ◽  
Vol 52 (3) ◽  
pp. 562-587 ◽  
Author(s):  
Jerome Dedecker ◽  
Jerome Dedecker ◽  
Florence Merlevede ◽  
Florence Merlevede
Keyword(s):  
Law Of Large Numbers ◽  
Convergence Rates ◽  
Large Numbers ◽  
Dependent Variables ◽  
The Law

The Bochner Mean Square Deviation and Law of Large Numbers for Squares of Random Elements in Banach Lattices

2002 ◽  
Vol 9 (1) ◽  
pp. 137-148
Author(s):  
Ivan Matsak ◽  
Anatolij Plichko
Keyword(s):  
Law Of Large Numbers ◽  
Function Spaces ◽  
Banach Lattices ◽  
Mean Square ◽  
Mean Square Deviation ◽  
Large Numbers ◽  
Random Elements ◽  
The Law

Abstract A Bochner mean square deviation for random elements of 2-convex Banach lattices is introduced and investigated. Results, analogous to the law of large numbers for squares of random elements are proved in some classes of Köthe function spaces.

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.

scholarly journals Deviation inequalities for Banach space valued martingales differences sequences and random fields

2019 ◽  
Vol 23 ◽  
pp. 922-946 ◽  
Author(s):  
Davide Giraudo
Keyword(s):  
Banach Space ◽  
Linear Regression ◽  
Random Field ◽  
Random Fields ◽  
Law Of Large Numbers ◽  
Partial Sums ◽  
Martingale Differences ◽  
Large Numbers ◽  
Deviation Inequalities ◽  
The Law

We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of an orthomartingale differences random field. These inequalities can be used to give rates for linear regression and the law of large numbers.

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