Removing divergences in the negative moments of the multi-fractal parition function with the wavelet transformation
We present a promising technique which is capable of accessing the divergence free component of the partition function for the negative moments of the multi-fractal analysis of data using the wavelet transformation. It is based on implicitly bounding the local logarithmic slope of the wavelet maxima lines between the values of the Holder exponent of the singularities which are accessible for the wavelet used. The method delivers correct and stable results, illustrated using a test example of the Besicovich measure analysed with the Mexican hat wavelet. The performance of the method is then shown as applied to real-life data.
|PROBABILITY AND STATISTICS (acm G.3), MODELS AND PRINCIPLES (acm H.1), PHYSICAL SCIENCES AND ENGINEERING (acm J.2)|
|Fractals (msc 28A80), Probabilistic methods, simulation and stochastic differential equations (msc 65Cxx), Stochastic differential and integral equations (msc 65C30), Computational Markov chains (msc 65C40), Other computational problems in probability (msc 65C50), Computational problems in statistics (msc 65C60)|
|Information (theme 2)|
|Information Systems [INS]|
Struzik, Z.R. (1998). Removing divergences in the negative moments of the multi-fractal parition function with the wavelet transformation. Information Systems [INS]. CWI.