Applied Probability Trust (April 6, 2008) EXPLICIT CONSTRUCTIONS OF OPERATOR SCALING STA- BLE RANDOM GAUSSIAN FIELDS

We propose an explicit way to generate a class of Operator scaling stable random Gaussian fields (OSSRGF). Such fields are anisotropic generalisations of self-similar fields. Indeed, they satisfy a scaling property {X(aEx)}x∈Rd L = {aHX(x)}x∈Rd. for some matrix E whose eigenvalues have a positive real part, and someH ∈ R. More specifically, we are able to construct any OSSRGF with stationary increments and with a spectral density (for any admissible E and H). Our construction provides- for simulations of texture as well as for detection of anisotropies in an image- a large class of models with anisotropic geometries and structures. We explicit the consequences in term of classification, simulation, and regularity of the sample paths of the fields