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Abstrakty
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.
Czasopismo
Rocznik
Tom
Strony
459--479
Opis fizyczny
Bibliogr. 53 poz.
Twórcy
autor
- Mathematical Institute, Heinrich-Heine-University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
autor
- Mathematical Institute, Heinrich-Heine-University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
Bibliografia
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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).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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