Unanticipated Features of the Multidimensional G-Normal Distribution

Abstract

In one dimension, the theory of the G-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 G-normal distribution.

Keywords: sublinear expectation; multi-dimensional G-normal distribution, independence