Random fractals and tree-indexed Markov chains | Zendy

Arnaud Durand | Zendy

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Random fractals and tree-indexed Markov chains

Author(s) -

Arnaud Durand

Publication year - 2009

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/590

Subject(s) - markov chain , tree (set theory) , fractal , mathematics , examples of markov chains , combinatorics , statistical physics , variable order markov model , markov model , statistics , physics , mathematical analysis

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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