Laws of Large Numbers for Arrays of Rowwise Negatively Associated Random Variables under Nonlinear Probabilities北大核心CSCD

In this paper, a strong law of large numbers for arrays of rowwise negatively associated random variables is obtained under nonlinear probabilities, from which Kolmogorov type and Marcinkiewicz–Zygmund type strong laws of large numbers are derived. And the notion of negative association is weaker than some existing notions of dependence in nonlinear probabilities. Furthermore, an extension of strong law of large numbers for arrays of rowwise independent random variables under nonlinear probabilities is obtained. As a special case, a Kolmogorov type strong law indicates that not only the cluster points of empirical averages lie in the interval between the lower expectation and upper expectation quasi-surely, but such an interval is also the smallest one that covers the empirical averages quasi-surely. Furthermore, the strong law also states that the upper and lower limits of the empirical averages will converge to the upper and lower expectations with upper probabilities one, respectively. © 2022 Chinese Academy of Sciences. All rights reserved.