Multifractal, a special class of complex self-affine processes, are under recent intensive investigations because of their fundamental nature and potential applications in diverse physical systems. Here, we report on a novel light scattering-based inverse method for extraction/quantification of multifractality in the spatial distribution of refractive index of biological tissues. The method is ...

Multifractal analyses of binary images of soil thin sections (STS) are widely used to characterize pore structure. However, no geometrical model is known to exist for a binary multifractal. Thus, the multifractality of binary images, and the accuracy of multifractal parameters estimated from them, need to be carefully evaluated. We captured 8-bit depth resolution digital grayscale images of thr...

To analyze financial time series exhibiting volatility clustering or other highly irregular behavior, we exploit multifractal detrended fluctuation analysis (MF-DFA). We summarize the use of local Hölder exponents, generalized Hurst exponents, and the multifractal spectrum in characterizing the way that the sample paths of a multifractal stochastic process exhibit lightor heavy-tailed fluctuati...

In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and scaling functions, and methods used in their determination by means of Wavelet Transform Modulus Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectru...

Previous multifractal spectrum theories can only reflect that an object is multifractal and few explicit expressions of f(α) can be obtained for the practical application of nonlinearity measure. In this paper, an analytical model for multifractal systems is developed by combining and improving the Jake model, Tyler fractal model and Gompertz curve, which allows one to obtain explicit expressio...

In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metr...

This paper presents the multifractal model of asset returns (“MMAR”), based upon the pioneering research into multifractal measures by Mandelbrot (1972, 1974). The multifractal model incorporates two elements of Mandelbrot’s past research that are now well-known in finance. First, the MMAR contains long-tails, as in Mandelbrot (1963), which focused on Lévy-stable distributions. In contrast to M...

Résumé Dans cet article nous allons présenter une méthode de détection d’objets basée sur l’analyse multifractale. La détection d’objets est particulièrement difficile lorsque l’on ne connaît pas les caractéristiques des objets pouvant être présents dans l’image. Contrairement aux méthodes le plus souvent proposées, cette méthode est destinée à détecter des objets artificiels dans des images ph...

The discovery of long-range dependence (a kind of asymptotic fractal scaling) in packet data from LANs and WANs, was followed by further work detailing evidence for multifractal behaviour in TCP/IP traffic in WANs. In terms of networking however, physical mechanisms for such behaviour have never been convincingly demonstrated, leaving open the question of whether multifractal traffic models are...