Revista Matemática Iberoamericana

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Volume 25, Issue 3, 2009, pp. 1089–1126
DOI: 10.4171/RMI/590

Published online: 2009-12-31

Random fractals and tree-indexed Markov chains

Arnaud Durand[1]

(1) Université Paris-Sud, Orsay, France

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.

Keywords: 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. Iberoam. 25 (2009), 1089-1126. doi: 10.4171/RMI/590