It is discussed by the use of simulations how the self-similar nature emerges in the computer network traffic. We propose a new model which incorporates the realistic communication procedure. In this model, the self-similarity is partially realized depending on the maximum data length and not on...

The influence of the1998 Russian financial crisis on the statistical properties of currencies in transition economies has been studied. Essential changes before and after crisis were discovered. All effects are essentially nonlinear and differ from the ones in advanced economies.

Zonation of time series into models which their parameters are piecewise constant are important and well-studied problems. Geophysical well logging data often show a complex pattern due to their multifractal nature. In a multifractal system, any pieces of it are established by a distinct...

Processes with long-range dependence (LRD) have gained wide applications in many fields of science and technologies ranging from hydrology to network traffic. Two key properties of such processes are LRD that is characterized by the Hurst parameter H and self-similarity (SS) that is measured by...

Fracture induced physical fields allow a real-time monitoring of damage evolution in materials during mechanical loading. We investigate the preparation of the recently occurred L’Aquila earthquake in terms of a detected precursory electromagnetic anomaly. The precursor is well described by a...

Within the framework of generalized combinatorial approaches, complexity is determined as a disorder measure for hierarchical statistical ensembles related to Cayley trees possessing arbitrary branching and number of levels. With strengthening hierarchical coupling, the complexity is shown to...

Applying fractal theory, this paper probes and discusses self-similarity and scale invariance of the Chinese stock market. It analyses three kinds of scale indexes, i.e., autocorrelation index, Hurst index and the scale index on the basis of detrended fluctuation analysis (DFA) algorithm and...

We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramér function, the...

Following the observations of the self-similarity in various length scales in the roughness of the fractured solid surfaces, we propose here a new model for the earthquake. We demonstrate rigorously that the contact area distribution between two fractal surfaces follows a unique power law. This...

Methods for estimating the fractal dimension, D, or the related Hurst coefficient, H, for a one-dimensional fractal series include Hurst's method of rescaled range analysis, spectral analysis, dispersional analysis, and scaled windowed variance analysis (which is related to detrended fluctuation...