Revista Matemática Iberoamericana

Random fractals and tree-indexed Markov chains

Arnaud Durand

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Abstract

We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the Moran-like deterministic or random recursive constructions considered by various authors. Among other applications, we consider various extensions of Mandelbrot's fractal percolation process.

Article information

Source
Rev. Mat. Iberoamericana, Volume 25, Number 3 (2009), 1089-1126.

Dates
First available in Project Euclid: 3 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1257258102

Mathematical Reviews number (MathSciNet)
MR2590694

Zentralblatt MATH identifier
1189.60030

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 28A80: Fractals [See also 37Fxx] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Hausdorff dimension random recursive constructions of fractals tree-indexed Markov chains branching processes in varying environment

Citation

Durand, Arnaud. Random fractals and tree-indexed Markov chains. Rev. Mat. Iberoamericana 25 (2009), no. 3, 1089--1126. https://projecteuclid.org/euclid.rmi/1257258102


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