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 Complete Moment Convergence for Sung’s Type Weighted Sums ofB-Valued Random Elements

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Wei Li ◽  
Pingyan Chen ◽  
Soo Hak Sung
Keyword(s):  
Law Of Large Numbers ◽  
Sufficient Conditions ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Real Numbers ◽  
Strong Law ◽  
Moment Convergence ◽  
Large Numbers ◽  
Random Elements ◽  
Necessary And Sufficient

Letp≥1/αand1/2<α≤1.Let{X,Xn,  n≥1}be a sequence of independent and identically distributedB-valued random elements and let{ani,  1≤i≤n,  n≥1}be an array of real numbers satisfying∑i=1naniq=O(n)for someq>p.We give necessary and sufficient conditions for complete moment convergence of the form∑n=1∞n(p-v)α-2E∑i=1naniXi-εnα+v<∞,  ∀ε>0, where0<v<p.A strong law of large numbers for weighted sums of independentB-valued random elements is also obtained.

scholarly journals Complete moment convergence for weighted sums of negatively orthant dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1195-1206 ◽  
Author(s):  
Xuejun Wang ◽  
Zhiyong Chen ◽  
Ru Xiao ◽  
Xiujuan Xie
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Strong Law ◽  
Associated Random Variables ◽  
Moment Convergence ◽  
Large Numbers

In this paper, the complete moment convergence and the integrability of the supremum for weighted sums of negatively orthant dependent (NOD, in short) random variables are presented. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for NODrandom variables are obtained. The results established in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.

scholarly journals Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Wenzhi Yang ◽  
Xinghui Wang
Keyword(s):  
Law Of Large Numbers ◽  
Convergence Rates ◽  
Type Theorem ◽  
Complete Moment Convergence ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Strong Law ◽  
Martingale Difference Sequence ◽  
Moment Convergence ◽  
Large Numbers

We study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011).

Some Remarks on Kolmogorov's Strong Law in Hilbert Spaces

1988 ◽  
Vol 37 (1-2) ◽  
pp. 91-94
Author(s):  
Anant P. Godbole
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Large Numbers

We consider a sequence [Formula: see text] of independent Hilbert-space valued random variables and extend the Hoffmann-Jorgensen and Pisier Strong Law of Large Numbers (SLLN) in a way similiar to Teicher's extension of the classical Kolmogorov SLLN.

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