Weak Law of Large Numbers Without Any Restriction on the Dependence Structure of Random Variables

2021 ◽  
Author(s):  
Habib Naderi ◽  
Przemysław Matuła ◽  
Mohammad Amini
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Dependence Structure ◽  
Large Numbers

scholarly journals Weak law of large numbers for randomly indexed sequences of m-dependent random variables

2020 ◽  
Vol 3 (4) ◽  
pp. 294-298
Author(s):  
Nhut Tan Nguyen ◽  
Tran Loc Hung
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Dependence Structure ◽  
Dependent Random Variables ◽  
Independent Sequence ◽  
Bounded Interval ◽  
Large Numbers ◽  
Dependent Sequence ◽  
The Right ◽  
Dependence Assumption

First, we establish the inequalities related to the upper bound for the probability of the sum of a random number of random variables satisfying certain conditions. More specifically, in Theorem 1, these variables are assumed that get values on a bounded interval and in particular, are setting under m-dependence assumption instead of the usual independence, where independence is merely the specific case of m-dependence when m equal to 0. For a random index with a familiar distribution, it is possible to proceed to make reasonable estimates for the expected terms on the right-hand side of the two inequalities in Theorem 1 to obtain Chernoff-Hoeffding-style bounds. Those bounds will be employed to prove that there is a weak law of large numbers for the sequence of m-dependent random variables correspondingly and the convergence rate is exponential. Next, in Theorem 2, we had chosen the Poisson distributed index as a typical for presentation. Finally, this theorem is illustrated through an image which is constructed by simulated values of 1-dependent variables. Here, the way that we have applied to create a 1-dependent sequence from an independent sequence that it is likely will help readers understand more about m-dependence structure.  

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.

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