Random fractals and tree-indexed Markov chains

Random fractals and tree-indexed Markov chains

Arnaud Durand

Source: Rev. Mat. Iberoamericana Volume 25, Number 3 (2009), 1089-1126.

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.

First Page: Show

Primary Subjects: 60D05

Secondary Subjects: 28A80, 60J10, 60J80

Keywords: Hausdorff dimension; random recursive constructions of fractals; tree-indexed Markov chains; branching processes in varying environment

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmi/1257258102
Zentralblatt MATH identifier: 05663371
Mathematical Reviews number (MathSciNet): MR2590694

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