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On the carrying dimension of occupation measures for self-affine random fields. (arXiv:1705.05676v1 [math.PR])
来源于:arXiv
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. Z\"ahle 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. 查看全文>>