Random wavelet series based on a tree-indexed Markov chain

Details Random wavelet series based on a tree-indexed Markov chain Random wavelet series based on a tree-indexed Markov chain

2007-09-22

arxiv.org/abs/0709.3597v1

Mathematics

Probability

25 pages

Scientific paper

10.1007/s00220-008-0504-7

We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a tree-indexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby performing their multifractal analysis. We also show that almost every sample path displays an oscillating singularity at almost every point and that the points at which a sample path has at most a given Holder exponent form a set with large intersection.

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