We study fractional Brownian motions in multifractal time, a model for multifractal processes proposed recently in the context of economics. Our interest focuses on the statistical properties of the wavelet decomposition of these processes, such as residual correlations (LRD) and stationarity, which are instrumental towards computing the statistics of wavelet-based estimators of the multifracta...

Fractal approach is successfully implemented in many applications within 2D signal processing. Fractal synthetical concept is applied for image compression with high compression ratios while fractal and multifractal descriptors provide classification of textural images with high occuracy. Various multifractal models are presented in literature. This paper summarizes them and illustrates new mul...

In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We give a complete multifractal analysis for Stern–Brocot intervals, for continued fractions and for certain Diophantine growth rates. In particular, we give detailed discussions of two multifractal spectra closely rela...

We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and fat-tailed distribution of the returns are considered as possible influence factors. The multifractal spectrum of the original return series is compared with ...

In this paper, we compare the portfolio allocation model of multifractal detrended Fluctuation approach with the modern efficient frontier model and the asset allocation model from Chinese institution fund, the risk-return performance of the multifractal detrended Fluctuation turns out to be more optimal portfolio allocation than that from Chinese institution fund and the conclusions have impli...

Source traffic streams as well as aggregated traffic flows often exhibit long-range-dependent (LRD) properties. In this paper, we model each traffic stream component through the multiplicative multifractal counting process traffic model. We prove that the superposition of a finite number of multiplicative multifractal traffic streams results in another multifractal stream. This property makes t...

This paper proposes a novel multifractal traffic model, and an associated parameter fitting procedure, based on stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. We provide a detailed comparison with a related multifractal model based on conservative cascades. Our results, that include applying the fitting procedure to real observed data ...

We prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures ^ of Markov type. For each value of a parameter a between a minimum amin and maximum amax, we define 'multifractal components' K^ a) of K, and show that they are fractals in the sense of Taylor. The dimension /(or) of K^ is computed from the data of the pro...

The scaling (fractal) characteristics of electrocardiograms (ECG) provide information complementary to traditional linear measurements (heart rate, repolarisation rate etc.) allowing them to discriminate signal changes induced pathologically or pharmacologically. Under such interventions scaling behaviour is described by multiple local scaling exponents and the signal is termed multifractal. Ex...

We establish a “conditional” variational principle, which unifies and extends many results in the multifractal analysis of dynamical systems. Namely, instead of considering several quantities of local nature and studying separately their multifractal spectra we develop a unified approach which allows us to obtain all spectra from a new multifractal spectrum. Using the variational principle we a...