Generalized Stable Multivariate Distribution and Anisotropic Dilations
chao-dyn
2019-08-17 v1 Chaotic Dynamics
Abstract
After having closely re-examined the notion of a L\'evy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a stable vector may not only have distinct Levy's stability indices 's, but the latter may depend on its norm. Indeed, we demonstrate that the Levy's stability index of a vector rather correspond to a linear application than to a scalar, and we show that the former should satisfy a simple spectral property.
Cite
@article{arxiv.chao-dyn/9912016,
title = {Generalized Stable Multivariate Distribution and Anisotropic Dilations},
author = {D. Schertzer and M. Larcheveque and J. Duan and S. Lovejoy},
journal= {arXiv preprint arXiv:chao-dyn/9912016},
year = {2019}
}