We investigate the sample paths regularity of operator scaling α-stable random fields. Such fields were introduced in [6] as anisotropic generalizations of self-similar fields and satisfy theIn the case of harmonizable operator scaling random fields, the sample paths are locally Hölderian and their Hölder regularity is characterized by the eigen decomposition of R d with respect to E. In particular, the directional Hölder regularity may vary and is given by the eigenvalues of E. In the case of moving average operator scaling random α-stable random fields, with α ∈ (0, 2) and d ≥ 2, the sample paths are almost surely discontinous.
Let X = {X(t), t ∈ R N } be a Gaussian random field with values in R d defined bywhere X 1 , . . . , X d are independent copies of a centered Gaussian random field X 0 . Under certain general conditions on X 0 , we study the hitting probabilities of X and determine the Hausdorff dimension of the inverse imageThe class of Gaussian random fields that satisfy our conditions includes not only fractional Brownian motion, the Brownian sheet, but also such anisotropic fields as fractional Brownian sheets, solutions to stochastic heat equation driven by space-time white noise and the operator-scaling Gaussian random fields with stationary increments constructed in [4].Running head: Inverse Images of Anisotropic Gaussian Random Fields 2000 AMS Classification numbers: 60G60; 60G15; 60G17; 28A80.
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