Mathematics – Probability
Scientific paper
2008-05-02
Mathematics
Probability
35 pages, 5 figures
Scientific paper
Multifractal analysis of multiplicative random cascades is revisited within the framework of {\em mixed asymptotics}. In this new framework, statistics are estimated over a sample which size increases as the resolution scale (or the sampling period) becomes finer. This allows one to continuously interpolate between the situation where one studies a single cascade sample at arbitrary fine scales and where at fixed scale, the sample length (number of cascades realizations) becomes infinite. We show that scaling exponents of ''mixed'' partitions functions i.e., the estimator of the cumulant generating function of the cascade generator distribution, depends on some ``mixed asymptotic'' exponent $\chi$ respectively above and beyond two critical value $p_\chi^-$ and $p_\chi^+$. We study the convergence properties of partition functions in mixed asymtotics regime and establish a central limit theorem. These results are shown to remain valid within a general wavelet analysis framework. Their interpretation in terms of Besov frontier are discussed. Moreover, within the mixed asymptotic framework, we establish a ``box-counting'' multifractal formalism that can be seen as a rigorous formulation of Mandelbrot's negative dimension theory. Numerical illustrations of our purpose on specific examples are also provided.
Bacry Emmanuel
Gloter Arnaud
Hoffmann Marc
Muzy Jean-Francois
No associations
LandOfFree
Multifractal analysis in a mixed asymptotic framework does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multifractal analysis in a mixed asymptotic framework, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multifractal analysis in a mixed asymptotic framework will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-340983