The Strong Law of Large Numbers for Sums of Independent Random Vectors with Operator Normalizations and Null Convergence of Gaussian Sequences

1988 ◽  
Vol 32 (2) ◽  
pp. 243-256 ◽  
Author(s):  
V. V. Buldygin ◽  
S. A. Solntsev
Keyword(s):  
Law Of Large Numbers ◽  
Random Vectors ◽  
Strong Law ◽  
Large Numbers

scholarly journals Convergence Theorems for m -Coordinatewise Negatively Associated Random Vectors in Hilbert Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Lyurong Shi
Keyword(s):  
Hilbert Spaces ◽  
Law Of Large Numbers ◽  
Linear Process ◽  
Random Coefficients ◽  
Complete Moment Convergence ◽  
Random Vectors ◽  
Strong Law ◽  
Negatively Associated ◽  
Moment Convergence ◽  
Large Numbers

In this study, some new results on convergence properties for m -coordinatewise negatively associated random vectors in Hilbert space are investigated. The weak law of large numbers, strong law of large numbers, complete convergence, and complete moment convergence for linear process of H-valued m -coordinatewise negatively associated random vectors with random coefficients are established. These results improve and generalise some corresponding ones in the literature.

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.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

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