Wavelet packet analysis was used to measure the global scaling behaviour of homogeneous fractal signals from the slope of decay for discrete wavelet coefficients belonging to the adapted wavelet best basis. A new scaling function for the size distribution correlation between wavelet coefficient energy magnitude and position in a sorted vector listing is described in terms of a power law to esti...

Electroencephalogram (EEG), the measures and records of the electrical activity of the brain, exhibits evidently nonlinear, non-stationary, chaotic and complex dynamic properties. Based on these properties, many nonlinear dynamical analysis techniques have emerged, and much valuable information has been extracted from complex EEG signals using these nonlinear analysis techniques. Among these te...

Information about fractal dimension is collected so that it can be applied to time series interpreting Hurst coefficient. The population size of a species is modelled as a dynamic system. The Hurst coefficient is calculated for these times series. A computer programme has been elaborated to compute the Hurst exponent of time series using the algorithms of range increment, second order moment in...

Fractional Brownian motion is known to be a realistic model for many natural rough surfaces. It is defined by means of a single parameter, the Hurst exponent, which determines the fractal characteristics of the surface. We propose a method to estimate the Hurst exponent of a fractional Brownian profile from the electromagnetic scattering data. The method is developed in the framework of three u...

We derive estimates for the solutions to differential equations driven by a Hölder continuous function of order β > 1/2. As an application we deduce the existence of moments for the solutions to stochastic partial differential equations driven by a fractional Brownian motion with Hurst parameter H > 1 2 .

Previous studies of the statistical behavior of solar flare waiting times are based on the assumptions of Gaussian and Poisson statistics, subject to central limit theorem restrictions. In this study, the results of a rescaled range analysis on the waiting times for two hard x-ray solar flare data sets are presented. The Hurst scaling parameter, H, for both data sets are well above 0.5, clearly...

This paper presents a novel discrete-time ATM traac model which exhibits a long range dependence character. The process results from the superposition of an innnite number of on/oo sources which have an increasing mean on and oo period duration. The condition under which the process has the long range dependence property is a simple function of the parameters of the on/oo sources. Moreover, the...

We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension d ≥ 3, started off either from a Poisson field or in equilibrium, when suitably normalised, converges to a Brownian motion in d ≥ 4. In d = 3, the limit process is fractional Brownian motion with Hurst parameter 3/4 when starting in equilibrium, and a related Gaussia...