Random recursive construction of self-similar fractal measures. The noncompact case
type: Item
instance of: scholarly article
title: Random recursive construction of self-similar fractal measures. The noncompact case
zbMATH Open document ID: 0723.60040
DOI: 10.1007/BF01192554
author: Matthias Arbeiter
publication date: 1991-01-01T00:00:00Z
review text: The self-similarity of sets (measures) is often defined in a constructive way. In the present paper it will be shown that the random recursive construction model of \textit{K. J. Falconer} [Math. Proc. Camb. Philos. Soc. 100, 559-582 (1986; Zbl 0623.60020)], \textit{S. Graf} [Probab. Theory Relat. Fields 74, 357-392 (1987; Zbl 0591.60005)], and \textit{R. D. Mauldin} and \textit{S. C. Williams} [Trans. Am. Math. Soc. 295, 325-346 (1986; Zbl 0625.54047)] for (statistically) self-similar sets may be generalized to the noncompact case. We define a sequence of random finite measures, which converges almost surely to a self-similar random limit measure. Under certain conditions on the generating Lipschitz maps we determine the carrying dimension of the limit measure.
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 4192774
zbMATH Keywords: self-similarity of sets
zbMATH Keywords: self-similar random limit measure
zbMATH Keywords: Lipschitz maps
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4192774