On the Strong Law of Large Numbers for Sequences of Dependent Random Variables with Finite Second Moments

2015 ◽  
Vol 206 (2) ◽  
pp. 197-206
Author(s):  
V. M. Korchevsky
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Second Moments ◽  
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.

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.

One-sided strong laws forincrements of sumsof i.i.d. random variables

2002 ◽  
Vol 39 (3-4) ◽  
pp. 333-359 ◽  
Author(s):  
A. N. Frolov
Keyword(s):  
Limit Theorems ◽  
Strong Approximation ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Moment Conditions ◽  
Second Moments ◽  
Large Numbers ◽  
Norming Sequence ◽  
Normal Law

We find a universal norming sequence in strong limit theorems for increments of sums of i.i.d. random variables with finite first moments and finite second moments of positive parts. Under various one-sided moment conditions our universal theorems imply the following results for sums and their increments: the strong law of large numbers, the law of the iterated logarithm, the Erdős-Rényi law of large numbers, the Shepp law, one-sided versions of the Csörgő-Révész strong approximation laws. We derive new results for random variables from domains of attraction of a normal law and asymmetric stable laws with index αЄ(1,2).

Sign in / Sign up

Export Citation Format

Share Document