Sample Path Properties of Operator-Slef-Similar Gaussian Random Fields

We study the Hausdorff dimension of the image and graph set, hitting probabilities, transience, and other sample path properties of certain isotropic operator-self-similar Gaussian random fields $X = \{X(t),\ t \in{\mathbf R}^N\}$ with stationary increments, including multiparameter operator fractional Brownian motion. Our results show that if $X({\mathbf 1})$, where ${\mathbf 1}=(1,0,\dots,0)\in{\mathbf R}^N$, is full, then many of such sample path properties are completely determined by the real parts of the eigenvalues of the self-similarity exponent $D$.