$\mathbf{G}$-Central limit theorems and $\mathbf{G}$-invariance principles for associated random variables
Probability
2022-05-31 v1
Abstract
The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of papers, we are going to set the general frame of the theory by considering an arbitrary infinitely decomposable (divisible) limit law for summands and study the associated functional laws converging to L\'evy processes. The asymptotic frame of Newman (1980) is still used as a main tool. Detailed results are given when is a Gaussian law (as confirmation of known results) and when is a Poisson law. In the later case, classical results for independent and identically distributed data are extended to stationary and non-stationary associated data.
Cite
@article{arxiv.2205.15102,
title = {$\mathbf{G}$-Central limit theorems and $\mathbf{G}$-invariance principles for associated random variables},
author = {Aladji Babacar Niang and Akym Adekpedjou and Harouna Sangaré and Gane Samb Lo},
journal= {arXiv preprint arXiv:2205.15102},
year = {2022}
}