Dimension Results for Space-anisotropic Gaussian Random Fields

Let X={X(t)∈Rd,t∈RN}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X= \{X(t) \in \mathbb{R}^d, t\in \mathbb{R}^N\}$$\end{document} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in ℝd, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.