Open AccessThe law of iterated logarithm for a class of random variables satisfying Rosenthal type inequality
Author(s) -
Hwanjo Yu,
Yong Zhang
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021642
Subject(s) - law of the iterated logarithm , mathematics , random variable , sequence (biology) , logarithm , type (biology) , combinatorics , iterated function , class (philosophy) , iterated logarithm , inequality , discrete mathematics , statistics , mathematical analysis , ecology , genetics , artificial intelligence , computer science , biology
Let $ \{Y_n, n\geq 1\} $ be sequence of random variables with $ EY_n = 0 $ and $ \sup_nE|Y_n|^p < \infty $ for each $ p > 2 $ satisfying Rosenthal type inequality. In this paper, the law of the iterated logarithm for a class of random variable sequence with non-identical distributions is established by the Rosenthal type inequality and Berry-Esseen bounds. The results extend the known ones from i.i.d and NA cases to a class of random variable satisfying Rosenthal type inequality.