On the Strong Law of Large Numbers for φ-Sub-Gaussian Random Variables

2021 ◽  
Author(s):  
K. Zajkowski
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Strong Law ◽  
Large Numbers

scholarly journals On the strong law of large numbers for ϕ-sub-Gaussian random variables

2021 ◽  
Vol 73 (3) ◽  
pp. 431-436
Author(s):  
K. Zajkowski
Keyword(s):  
Natural Number ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Random Variable ◽  
Gaussian Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

UDC 517.9 For let if and if . For a random variable ξ let denote ; is a norm in a space - subgaussian random variables. We prove that if for a sequence there exist positive constants and such that for every natural number the following inequality holds then converges almost surely to zero as . This result is a generalization of the strong law of large numbers for independent sub-Gaussian random variables [see R. L. Taylor, T.-C. Hu, <em>Sub-Gaussian techniques in proving strong laws of large numbers</em>, Amer. Math. Monthly, <strong>94</strong>, 295 – 299 (1987)] to the case of dependent -sub-Gaussian random variables.

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.

A Note on the Strong Law of Large Numbers

1994 ◽  
Vol 44 (1-2) ◽  
pp. 115-122 ◽  
Author(s):  
Arup Bose ◽  
Tapas K. Chandra
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Large Numbers

Let { X n} be a sequence of pairwise independent (or -mixing) mean zero random variables such that [Formula: see text] is integrable on (0,∞) and [Formula: see text] then we show that [Formula: see text] almost surely as n→∞, These are very convenient and immediate generalizations of the classical SLLN for the iid case.

scholarly journals Law of large numbers for the sequence of uncorrelated fuzzy random variables

2021 ◽  
pp. 1-8
Author(s):  
Li Guan ◽  
Jinping Zhang ◽  
Jieming Zhou
Keyword(s):  
Law Of Large Numbers ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Fuzzy Random Variables ◽  
Strong Law ◽  
Fuzzy Variables ◽  
Large Numbers ◽  
The Law ◽  
Fuzzy Random

This work proposes the concept of uncorrelation for fuzzy random variables, which is weaker than independence. For the sequence of uncorrelated fuzzy variables, weak and strong law of large numbers are studied under the uniform Hausdorff metric d H ∞ . The results generalize the law of large numbers for independent fuzzy random variables.

Laws of large numbers for q-dependent random variables and nonextensive statistical mechanics

2017 ◽  
Vol 31 (15) ◽  
pp. 1750117
Author(s):  
Marco A. S. Trindade
Keyword(s):  
Statistical Mechanics ◽  
Stochastic Processes ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Nonextensive Statistical Mechanics ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers

In this work, we prove a weak law and a strong law of large numbers through the concept of [Formula: see text]-product for dependent random variables, in the context of nonextensive statistical mechanics. Applications for the consistency of estimators are presented and connections with stochastic processes are discussed.

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