@article{Wu2024, 
author = {Qingfeng Wu and Xili Tan and Shuang Guo and Peiyu Sun},
title = {Strong law of large numbers for weighted sums of  m-widely acceptable random variables under sub-linear expectation space},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {29773-29805},
keywords = {m-widely acceptable random variables, strong law of large numbers, sublinear expectation space, slowly varying function, almost surely convergence},
url = {https://www.sciopen.com/article/10.3934/math.20241442},
doi = {10.3934/math.20241442},
abstract = {In this article, using the Fuk-Nagaev type inequality, we studied general strong law of large numbers for weighted sums of  m-widely acceptable ( m-WA, for short) random variables under sublinear expectation space with the integral condition   E^(f−(|X|))≤CV(f−(|X|))<∞and  Choquet integrals existence, respectively, where   f(x)=x1/βL(x)for  β>1,  L(x)>0  (x>0) was a monotonic nondecreasing slowly varying function, and  f−(x) was the inverse function of  f(x). One of the results included the Kolmogorov-type strong law of large numbers and the partial Marcinkiewicz-type strong law of large numbers for  m-WA random variables under sublinear expectation space. Besides, we obtained almost surely convergence for weighted sums of  m-WA random variables under sublinear expectation space. These results improved the corresponding results of Ma and Wu under sublinear expectation space.}
}