Random fractals and tree-indexed Markov chains

Details Random fractals and tree-indexed Markov chains Random fractals and tree-indexed Markov chains

2007-09-22

arxiv.org/abs/0709.3598v1

Mathematics

Probability

30 pages

Scientific paper

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.

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