Maximal inequalities for demimartingales and a strong law of large numbers

2000 ◽  
Vol 50 (4) ◽  
pp. 357-363 ◽  
Author(s):  
Tasos C. Christofides
Keyword(s):  
Law Of Large Numbers ◽  
Strong Law ◽  
Maximal Inequalities ◽  
Large Numbers

Maximal inequalities for N-demimartingale and strong law of large numbers

2011 ◽  
Vol 81 (9) ◽  
pp. 1348-1353 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
B.L.S. Prakasa Rao ◽  
Wenzhi Yang
Keyword(s):  
Law Of Large Numbers ◽  
Strong Law ◽  
Maximal Inequalities ◽  
Large Numbers

General maximal inequalities related to the strong law of large numbers

2007 ◽  
Vol 81 (1-2) ◽  
pp. 85-96 ◽  
Author(s):  
S. Levental ◽  
H. Salehi ◽  
S. A. Chobanyan
Keyword(s):  
Law Of Large Numbers ◽  
Strong Law ◽  
Maximal Inequalities ◽  
Large Numbers

Strong Laws for Dependent Heterogeneous Processes

1991 ◽  
Vol 7 (2) ◽  
pp. 213-221 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Law Of Large Numbers ◽  
Strong Mixing ◽  
Strong Law ◽  
Strong Laws ◽  
Maximal Inequalities ◽  
Large Numbers ◽  
Heterogeneous Processes ◽  
Mixing Sequences ◽  
Strong Mixing Sequences ◽  
Weakly Dependent

This paper presents maximal inequalities and strong law of large numbers for weakly dependent heterogeneous random variables. Specifically considered are Lr mixingales for r > 1, strong mixing sequences, and near epoch dependent (NED) sequences. We provide the first strong law for Lr-bounded Lr mixingales and NED sequences for 1 > r > 2. The strong laws presented for α-mixing sequences are less restrictive than the laws of McLeish [8].

Two-parameter strong laws and maximal inequalities for U-statistics

1987 ◽  
Vol 107 (1-2) ◽  
pp. 133-151 ◽  
Author(s):  
Terry R. McConnell
Keyword(s):  
Law Of Large Numbers ◽  
Weak Type ◽  
Sufficient Conditions ◽  
Strong Law ◽  
Strong Laws ◽  
Maximal Inequalities ◽  
U Statistics ◽  
Large Numbers ◽  
Necessary And Sufficient ◽  
Two Parameter

SynopsisWe provide necessary and sufficient conditions for two-parameter convergence in the strong law of large numbers for U-statistics. We also obtain weak-type (1,1) inequalities for one and two-sample U-statistics of order 2 which are, in a sense, best possible.

scholarly journals MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES

2011 ◽  
Vol 26 (1) ◽  
pp. 151-161 ◽  
Author(s):  
Wang Xuejun ◽  
Hu Shuhe ◽  
Li Xiaoqin ◽  
Yang Wenzhi
Keyword(s):  
Law Of Large Numbers ◽  
Strong Law ◽  
Maximal Inequalities ◽  
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.

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