Generalized random recursive constructions and geometric properties of random fractals

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 di...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 267; no. 1; pp. 65 - 76
Main Authors Liu, Yan-Yan, Wen, Zhi-Ying, Wu, Jun
Format Journal Article
LanguageEnglish
Published Berlin WILEY-VCH Verlag 01.04.2004
WILEY‐VCH Verlag
Subjects
Generalized random Moran construction
Hausdorff dimension
martingale
moments
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Summary: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)
Bibliography:istex:327BA2DBB0975DF12304E628D8F31067FB97E961
ArticleID:MANA200310153
ark:/67375/WNG-HJQF1G21-4
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ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200310153