H\"{o}lder regularity for operator scaling stable random fields
Probability
2016-08-14 v1
Abstract
We investigate the sample paths regularity of operator scaling alpha-stable random fields. Such fields were introduced as anisotropic generalizations of self-similar fields and satisfy a scaling property for a real matrix E. In the case of harmonizable operator scaling random fields, the sample paths are locally H\"{o}lderian and their H\"{o}lder regularity is characterized by the eigen decomposition with respect to E. In particular, the directional H\"{o}lder regularity may vary and is given by the eigenvalues of E. In the case of moving average operator scaling random alpha-stable random fields, with 0<alpha<2, the sample paths are almost surely discontinous.
Cite
@article{arxiv.math/0702050,
title = {H\"{o}lder regularity for operator scaling stable random fields},
author = {Hermine Biermé and Céline Lacaux},
journal= {arXiv preprint arXiv:math/0702050},
year = {2016}
}