scholarly journals The strong law of large numbers for L-statistics with dependent data

2006 ◽  
Vol 47 (6) ◽  
pp. 975-979 ◽  
Author(s):  
E. A. Baklanov
Keyword(s):  
Law Of Large Numbers ◽  
Dependent Data ◽  
Strong Law ◽  
Large Numbers

scholarly journals Marcinkiewicz law of large numbers for outer products of heavy-tailed, long-range dependent data

2016 ◽  
Vol 48 (2) ◽  
pp. 349-368
Author(s):  
Michael A. Kouritzin ◽  
Samira Sadeghi
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Law Of Large Numbers ◽  
Nonlinear Function ◽  
Dependent Data ◽  
Long Range Dependence ◽  
Linear Processes ◽  
Strong Law ◽  
Large Numbers ◽  
Heavy Tailed

Abstract The Marcinkiewicz strong law, limn→∞(1 / n1/p)∑k=1n(Dk - D) = 0 almost surely with p ∈ (1, 2), is studied for outer products Dk = {XkX̅kT}, where {Xk} and {X̅k} are both two-sided (multivariate) linear processes (with coefficient matrices (Cl), (C̅l) and independent and identically distributed zero-mean innovations {Ξ} and {Ξ̅}). Matrix sequences Cl and C ̅l can decay slowly enough (as |l| → ∞) that {Xk,X ̅k} have long-range dependence, while {Dk} can have heavy tails. In particular, the heavy-tail and long-range-dependence phenomena for {Dk} are handled simultaneously and a new decoupling property is proved that shows the convergence rate is determined by the worst of the heavy tails or the long-range dependence, but not the combination. The main result is applied to obtain a Marcinkiewicz strong law of large numbers for stochastic approximation, nonlinear function forms, and autocovariances.

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.

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