H\"{o}lder regularity for operator scaling stable random fields

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.