Functional central limit theorems for random vectors under sub-linear expectations
Probability
2019-12-11 v1
Abstract
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under the sub-linear expectation by Zhang (2019). In this paper, we consider the multi-dimensional martingale like random vectors and establish a functional central limit theorem. As applications, the Lindeberg central limit theorem for independent random vectors is established, and the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are obtained.
Cite
@article{arxiv.1912.04715,
title = {Functional central limit theorems for random vectors under sub-linear expectations},
author = {Li-Xin Zhang},
journal= {arXiv preprint arXiv:1912.04715},
year = {2019}
}
Comments
24 pages. arXiv admin note: text overlap with arXiv:1611.01619