Geodesic
Sample Path Properties of Operator-Slef-Similar Gaussian Random Fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 94-116

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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 $D$.
Keywords: operator-self-similar Gaussian random fields, graph, polar set, transience.
Mots-clés : image, Hausdorff dimension 
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     title = {Sample {Path} {Properties} of {Operator-Slef-Similar} {Gaussian} {Random} {Fields}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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J. D. Mason; Xiao Yimin. Sample Path Properties of Operator-Slef-Similar Gaussian Random Fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 94-116. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a4/