## Revista Matemática Iberoamericana

### Random fractals and tree-indexed Markov chains

Arnaud Durand

#### 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

https://projecteuclid.org/euclid.rmi/1257258102

Mathematical Reviews number (MathSciNet)
MR2590694

Zentralblatt MATH identifier
1189.60030

#### 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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