Comparing the $G$-Normal Distribution to its Classical Counterpart
Probability
2014-12-04 v2 Mathematical Finance
Abstract
In one dimension, the theory of the -normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been discovered is quite nonintuitive. By answering several classically-inspired questions concerning independence, covariance uncertainty, and behavior under certain linear operations, we continue to highlight the fascinating range of unexpected attributes of the multidimensional -normal distribution.
Cite
@article{arxiv.1407.5139,
title = {Comparing the $G$-Normal Distribution to its Classical Counterpart},
author = {Erhan Bayraktar and Alexander Munk},
journal= {arXiv preprint arXiv:1407.5139},
year = {2014}
}
Comments
Final version. To appear in Communications on Stochastic Analysis. Title has changed. Keywords: sublinear expectation, multidimensional $G$-normal distribution, independence