Complete convergence and complete moment convergence for randomly weighted sums of widely negative dependent random variables under sublinear expectations

M. M. Wang, X. J. Wang

School of Big Data and Statistics, Anhui University, Hefei, P. R. China

Abstract: It is well known that the convergence properties for weighted sums of random variables are important topics in probability limit theory. In this paper, under some suitable conditions, we study the complete convergence and complete moment convergence for randomly weighted sums of arrays of rowwise widely negative dependent random variables in sublinear expectation space, which extend the corresponding ones in classical probability space to the case of sublinear expectation space. As an application, we obtain strong law of large numbers for the randomly weighted sums of arrays of rowwise widely negative dependent random variables.

Keywords: widely negative dependent random variable, complete convergence, complete moment convergence, sublinear expectation space.

Received: 01.10.2023
Revised: 16.02.2025

DOI: 10.4213/tvp5730

 English version: Theory of Probability and its Applications, 2025, 70:3, 397–416

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