Complete Convergence and the Law of Large Numbers

1983 ◽  
pp. 229-240 ◽  
Author(s):  
P. L. Hsu ◽  
Herbert Robbins
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
The Law

COMPLETE CONVERGENCE FOR ARRAYS AND THE LAW OF THE SINGLE LOGARITHM

2017 ◽  
Vol 96 (2) ◽  
pp. 333-344
Author(s):  
ALLAN GUT ◽  
ULRICH STADTMÜLLER
Keyword(s):  
Limit Theorems ◽  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Almost Sure Convergence ◽  
Strong Law ◽  
Moment Conditions ◽  
Large Numbers ◽  
Distributed Arrays ◽  
The Law ◽  
Independent And Identically Distributed

The present paper is devoted to complete convergence and the strong law of large numbers under moment conditions near those of the law of the single logarithm (LSL) for independent and identically distributed arrays. More precisely, we investigate limit theorems under moment conditions which are stronger than $2p$ for any $p<2$, in which case we know that there is almost sure convergence to 0, and weaker than $E\,X^{4}/(\log ^{+}|X|)^{2}<\infty$, in which case the LSL holds.

Complete convergence and the law of large numbers for arrays of random elements

1997 ◽  
Vol 30 (7) ◽  
pp. 4257-4266 ◽  
Author(s):  
Tien-Chung Hu ◽  
Hen-Chao Chang
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
Random Elements ◽  
The Law

scholarly journals A new proof for the generalized law of large numbers under Choquet expectation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jing Chen ◽  
Zengjing Chen
Keyword(s):  
Probability Theory ◽  
Law Of Large Numbers ◽  
Moment Condition ◽  
Large Numbers ◽  
Choquet Expectation ◽  
The Law ◽  
Linear Probability ◽  
First Moment ◽  
Independent And Identically Distributed

Abstract In this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions. This generalizes the Linderberg–Feller methodology for linear probability theory to Choquet expectation framework and extends the law of large numbers under Choquet expectation from the strong independent and identically distributed (iid) assumptions to the convolutional independence combined with the strengthened first moment condition.

Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

2006 ◽  
Vol 73 (4) ◽  
pp. 673-686 ◽  
Author(s):  
M. A. Milevsky ◽  
S. D. Promislow ◽  
V. R. Young
Keyword(s):  
Mortality Risk ◽  
Law Of Large Numbers ◽  
Sharpe Ratio ◽  
Risk Premiums ◽  
Large Numbers ◽  
The Law
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