Operator scaling stable random fields

A scalar valued random field (X(x)}(x is an element of Rd) is called operator-scaling if for some d x d matrix E with positive real parts of the eigenvalues and some H > 0 we have {X(c(E)x)}(x is an element of Rd) =f.d. {c(H) X (x)}(x is an element of Rd) for all c > 0, where =(f.d). 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(c(E)x) = c phi(x). These fields also have stationary increments and are stochastically continuous. In the Gaussian case, critical Holder-exponents and the Hausdorff-dimension of the sample paths are also obtained. (C) 2006 Elsevier B.V. All rights reserved.