1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, P. R. China;2. School of Science, Jimei University, Xiamen 361021, P. R. China
Abstract:
Let
$$X= \{X(t) \in \mathbb{R}^d, t\in \mathbb{R}^N\}$$
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.