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Vo Thi Van Anh; Nguyen Le Bao Khuyen

doi:10.54644/jte.64.2021.50

Authors

Vo Thi Van Anh HCMC University of Technology and Education, Vietnam
Nguyen Le Bao Khuyen Kien Giang Medical College, Vietnam

Corressponding author's email:

anhvtv@hcmute.edu.vn

DOI:

https://doi.org/10.54644/jte.64.2021.50

Keywords:

negatively superadditive dependent, stochastically dominated, law of large numbers, regularly varying, convergence in probability

Abstract

The limit theorems, especially the theorems of the law of large numbers, play a very important role in the theory of probability and mathematical statistics. Law of the large number established by Bernoulli in 1713 was the origin of the modern probability theory based now on the solid axiomatic foundation proposed by Kolmogorov in 1933. There are a number of brilliant results concerning the law of large numbers in weak and strong forms. Among them one can mention, e.g., the Kolmogorov theorem for independent identically distributed random variables, the results by Khintchine, Feller, Birkhoff, Prohorov, Petrov, Martikainen, Gut and many other researchers. The general trend is to extend the classical results by analysis of dependent summands, such as martingale dependence, Markov dependence, m-dependence, blockwise m-dependence, negative quadrant dependence, negatively association, and negatively superadditive dependence. In this paper, we give a version of the Kolmogorov - Feller law of the large number for negatively superadditive dependent random variables and stochastically dominated random variables.

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