On the carrying dimension of occupation measures for selfaffine random fields
Abstract
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 selfaffine random fields. We present a close relationship between the carrying dimension of the corresponding selfaffine random occupation measure introduced by U. Zähle and the Hausdorff dimension of the graph of selfaffine fields. In the case of exponential scaling operators, the dimension formula can be explicitly calculated by means of the singular value function. This also enables to get a lower bound for the Hausdorff dimension of the range of general selfaffine random fields under mild regularity assumptions.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 DOI:
 10.48550/arXiv.1705.05676
 arXiv:
 arXiv:1705.05676
 Bibcode:
 2017arXiv170505676K
 Keywords:

 Mathematics  Probability
 EPrint:
 Probab. Math. Statist. 39(2), 2019, 459479