Revista Matemática Iberoamericana

Random fractals and tree-indexed Markov chains

Arnaud Durand

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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

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

First available in Project Euclid: 3 November 2009

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Zentralblatt MATH identifier

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.)

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


Durand, Arnaud. Random fractals and tree-indexed Markov chains. Rev. Mat. Iberoamericana 25 (2009), no. 3, 1089--1126.

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