scholarly journals A Gambler that Bets Forever and the Strong Law of Large Numbers

Author(s):  
Calvin Wooyoung Chin
2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu

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.


1994 ◽  
Vol 44 (1-2) ◽  
pp. 115-122 ◽  
Author(s):  
Arup Bose ◽  
Tapas K. Chandra

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.


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