Operator scaling stable random fields

A scalar valued random field is called operator-scaling if for some dxd matrix E with positive real parts of the eigenvalues and some H>0 we have where denotes equality of all finite-dimensional marginal distributions. We present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing so called E-homogeneous functions [phi], satisfying [phi](cEx)=c[phi](x). These fields also have stationary increments and are stochastically continuous. In the Gaussian case, critical Hölder-exponents and the Hausdorff-dimension of the sample paths are also obtained.