This article is cited in 51 papers

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

J. D. Mason^a, Xiao Yimin<sup>b

a</sup> University of Utah, Department of Mathematics
^b Michigan State University, Department of Statistics and Probability

Abstract: 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, image, graph, Hausdorff dimension, polar set, transience.

Received: 07.04.1999

Language: English

DOI: 10.4213/tvp3953

 English version: Theory of Probability and its Applications, 2002, 46:1, 58–78

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