标题： 各向异性高斯随机场的极集 显示英文标题

标题： Polar sets of anisotropic Gaussian random fields

摘要： 本文研究各向异性高斯随机场的极集，即高斯随机场几乎肯定不会触及的集合。主要假设是协方差矩阵的特征值从下方有界，并且与高斯随机场相关的典范度量被一个各向异性度量支配。我们推导出命中概率的一个上界，并得出小Hausdorff维数的集合是极集的结论。此外，这些结果允许通过一个随机场平移高斯随机场，该随机场独立于高斯随机场，并且其样本函数具有有界的Hölder范数。 显示英文摘要

摘要： This paper studies polar sets of anisotropic Gaussian random fields, i.e. sets which a Gaussian random field 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 field is dominated by an anisotropic metric. We deduce an upper bound for the hitting probabilities and conclude that sets with small Hausdorff dimension are polar. Moreover, the results allow for a translation of the Gaussian random field by a random field, that is independent of the Gaussian random field and whose sample functions are of bounded H\"older norm.