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Generalized random recursive constructions and geometric properties of random fractals

✍ Scribed by Yan-Yan Liu; Zhi-Ying Wen; Jun Wu

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
184 KB
Volume
267
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We study random recursive constructions in which the contracting vectors have different distributions at different stages. With such constructions, the one parameter family of martingales are introduced and the probabilistic behaviours of the limit random objects (not identically distributed) are discussed. We prove that the random fractal associated with such construction has a constant Hausdorff dimension almost surely and give an explicit formula to determine it. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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