The Brunk–Prokhorov strong law of large numbers for fields of martingale differences taking values in a Banach space

2013 ◽  
Vol 83 (8) ◽  
pp. 1901-1910 ◽  
Author(s):  
Ta Cong Son ◽  
Dang Hung Thang
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Martingale Differences ◽  
Strong Law ◽  
Large Numbers

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.

Sample Behavior and Laws of Large Numbers for Gaussian Random Elements

2003 ◽  
Vol 10 (4) ◽  
pp. 637-676
Author(s):  
Z. Ergemlidze ◽  
A. Shangua ◽  
V. Tarieladze
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

Abstract Criteria for almost sure boundedness and convergence to zero almost surely of Banach space valued independent Gaussian random elements are found. The obtained statements can be viewed as vector-valued versions of the corresponding results due to N. Vakhania. Moreover, from the obtained statements a strong law of large numbers is derived in the form of Yu. V. Prokhorov.

scholarly journals Strong Laws of Large Numbers for𝔹-Valued Random Fields

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Zbigniew A. Lagodowski
Keyword(s):  
Banach Space ◽  
Random Fields ◽  
Law Of Large Numbers ◽  
Random Vectors ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Geometry Of Banach Space ◽  
Necessary And Sufficient

We extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) for𝔹-valued random vectors under geometric assumptions. Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic conditions for the geometry of Banach space associated to the strong and weak law of large numbers for multidimensionally indexed random vectors.

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