A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers

2021 ◽  
pp. 109181
Author(s):  
Andrew Rosalsky ◽  
Lê Vǎn Thành
Keyword(s):  
Law Of Large Numbers ◽  
Uniform Integrability ◽  
Stochastic Domination ◽  
Strong Law ◽  
Large Numbers

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 A NONCONVENTIONAL STRONG LAW OF LARGE NUMBERS AND FRACTAL DIMENSIONS OF SOME MULTIPLE RECURRENCE SETS

2012 ◽  
Vol 12 (03) ◽  
pp. 1150023 ◽  
Author(s):  
YURI KIFER
Keyword(s):  
Law Of Large Numbers ◽  
Fractal Dimensions ◽  
Growth Conditions ◽  
Multiple Recurrence ◽  
Strong Law ◽  
Moment Conditions ◽  
Vector Process ◽  
Regularity Properties ◽  
Large Numbers ◽  
Positive Functions

We provide conditions which yield a strong law of large numbers for expressions of the form [Formula: see text] where X(n), n ≥ 0's is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polinomial growth and certain regularity properties and qi, i > m are positive functions taking on integer values on integers with some growth conditions. Applying these results we study certain multifractal formalism type questions concerning Hausdorff dimensions of some sets of numbers with prescribed asymptotic frequencies of combinations of digits at places q1(n), …, qℓ(n).

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