On the carrying dimension of occupation measures for self-affine 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 self-affine random fields. We present a close relationship between the carrying dimension of the corresponding self-affine random occupation measure introduced by U. Zähle and the Hausdorff dimension of the graph of self-affine 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 self-affine random fields under mild regularity assumptions.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2017
- DOI:
- 10.48550/arXiv.1705.05676
- arXiv:
- arXiv:1705.05676
- Bibcode:
- 2017arXiv170505676K
- Keywords:
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- Mathematics - Probability
- E-Print:
- Probab. Math. Statist. 39(2), 2019, 459-479