论文标题
各向异性高斯随机字段：达到概率和应用的标准
Anisotropic Gaussian random fields: Criteria for hitting probabilities and applications
论文作者
论文摘要
我们制定了针对各向异性高斯随机场与一类规范函数给出的相关规范伪金属的概率的标准。这分别从容量和Hausdorff度量的一般概念方面产生了上限和上限，因此以Bessel-Riesz的能力和$γ$维的Hausdorff度量扩展了经典估计。我们将标准应用于线性随机偏微分方程系统，该方程是由时空噪声驱动的，这些时空噪声是时间分数，白色或在太空中有色。
We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class of gauge functions. This yields lower and upper bounds in terms of general notions of capacity and Hausdorff measure, respectively, therefore extending the classical estimates with the Bessel-Riesz capacity and the $γ$-dimensional Hausdorff measure. We apply the criteria to a system of linear stochastic partial differential equations driven by space-time noises that are fractional in time and either white or colored in space.
