On the carrying dimension of occupation measures for self-affine random fields
DOI:
https://doi.org/10.19195/0208-4147.39.2.12Słowa kluczowe:
Random measure, occupation measure, self-affinity, random field, operator self-similarity, range, graph, operator semistable, Hausdorff dimension, carrying dimension, singular value functionAbstrakt
Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for the sample functions of a large class of self-affine random fields. The aim is to demonstrate the following interesting relation to a series of articles by U. Zähle 1984, 1988, 1990, 1991. Under natural regularity assumptions, we prove that the Hausdorff dimension of the graph of self-affine fields coincides with the carrying dimension of the corresponding self-affine random occupation measure introduced by U. Zähle. As a remarkable consequence we obtain a general formula for the Hausdorff dimension given by means of the singular value function.
