This paper is concerned with sample path properties of anisotropic Gaussian random fields. We establish Fernique-type inequalities and utilize them to study the global and local moduli of continuity for anisotropic Gaussian random fields. Applications to fractional Brownian sheets and to the solutions of stochastic partial differential equations are investigated.

中文翻译：

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各向异性高斯随机场的 Fernique 型不等式和连续性模

本文关注的是各向异性高斯随机场的样本路径特性。我们建立 Fernique 型不等式并利用它们来研究各向异性高斯随机场的全局和局部连续性模。研究了分数布朗表和随机偏微分方程的解的应用。