Polar sets of anisotropic Gaussian random fields

This paper studies polar sets of anisotropic Gaussian random elds, i.e. sets which a Gaussian random eld does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical metric associated with the Gaussian random eld is dominated by an anisotropic metric. We deduce an upper bound for the hitting probabilities and conclude that sets with small Hausdor dimension are polar. Moreover, the results allow for a translation of the Gaussian random eld by a random eld, that is independent of the Gaussian random eld and whose sample functions are of bounded Hölder norm. -- Anisotropic Gaussian fields ; Hitting probabilities ; Polar sets ; Hausdorff dimension ; European option ; Jump diffusion ; Calibration