Random fractals and tree-indexed Markov chains. (English) Zbl 1189.60030

Durand, Arnaud

Rev. Mat. Iberoam. 25, No. 3, 1089-1126 (2009).

Author’s 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 construction considered by various authors. Among other applications, we consider various extensions of Mandelbrot’s fractal percolation process.

Reviewer: Ilya S. Molchanov (Bern)

MSC:

60D05	Geometric probability and stochastic geometry
28A80	Fractals
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 construction of fractals; tree-indexed Markov chain; branching processes in varying environment

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