On the Carrying Dimension of Occupation Measures for Self-Affine Random Fields

• Autorzy: Kern Peter , Sönmez Ercan

Identyfikatory

DOI

10.19195/0208-4147.39.2.12

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

random measure; occupation measure; self-affinity; random field; operator self-similarity; range; graph; operator semistable; Hausdorff dimension; carrying dimension; singular value function

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 459--479
• Opis fizyczny: Bibliogr. 53 poz.

Twórcy

autor

Kern Peter

• Mathematical Institute, Heinrich-Heine-University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany

autor

Sönmez Ercan

• Mathematical Institute, Heinrich-Heine-University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).