An optimality results about sample paths properties of Operator Scaling Gaussian Random Fields in anisotropic Besov spaces

Marianne Clausel (1) , Béatrice Vedel (2)

1 SAM - Statistique Apprentissage Machine
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We study the sample paths properties of Operator scaling Gaussian random fields. Such fields are anisotropic generalizations of anisotropic self-similar random fields as anisotropic Fractional Brownian Motion. Some characteristic properties of the anisotropy are revealed by the regularity of the sample paths. The sharpest way of measuring smoothness is related to these anisotropies and thus to the geometry of these fields

Mots clés: Operator scaling Gaussian random field; anisotropy; sample paths properties; anisotropic Besov spaces

Domaines: Analyse fonctionnelle [math.FA]; Probabilités [math.PR]

Marianne Clausel, Béatrice Vedel. An optimality results about sample paths properties of Operator Scaling Gaussian Random Fields in anisotropic Besov spaces. Annals of the University of Bucharest. Mathematical series, 2013, 4 (LXII), pp.375-409. ⟨hal-00918550⟩