Almost Sure Central Limit Theorem in Sub-linear Expectation Spaces
Probability
2018-10-19 v3
Abstract
Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure central limit theorem under sub-linear expectations in this paper, which is a quasi sure convergence version of Peng's central limit theorem. Moreover, this result is a natural extension of the classical almost sure central limit theorem to the case where the probability is no longer additive. Meanwhile, we prove a new kind of strong law of large numbers for non-additive probabilities without the independent identically distributed assumption.
Cite
@article{arxiv.1804.09971,
title = {Almost Sure Central Limit Theorem in Sub-linear Expectation Spaces},
author = {Weihuan Huang and Panyu Wu},
journal= {arXiv preprint arXiv:1804.09971},
year = {2018}
}