Operator Scaling Stable Random Fields

Abstract

A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing so called E-homogeneous functions. These fields also have stationary increments and are stochastically continuous. In the Gaussian case critical H\"{o}lder-exponents and the Hausdorff-dimension of the sample paths are also obtained.