We investigate the departure process of an ATM output buffer intaking asymptotically second-order self-similar traffic using matrix-analytic technique. The results obtained include the marginal and joint distribution of interdeparture times. We show that output and input processes asymptotically possess the same tail and smoothing effect takes place only for traffic with small Hurst parameters.

The conventional formal tool to detect effects of the financial persistence is in terms of the Hurst exponent. A typical corresponding result is that its value comes out close to 0.5, as characteristic for geometric Brownian motion, with at most small departures from this value in either direction depending on the market and on the time scales involved. We study the high frequency price changes...

Stylized facts of empirical assets log-returns Z include the existence of (semi) heavy tailed distributions fZ(z) and a non-linear spectrum of Hurst exponents τ (β). Empirical data considered are daily prices of 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is driven by expectations. The model is a multiplicative random process with a stocha...

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...

[1] Climate variations on timescales longer than a year are often characterized by temporal scaling (‘‘power-law’’) behavior for which spectral power builds up at low frequencies, in contrast to red-noise behavior for which spectral power saturates at low frequencies. Checks on the ability of climate prediction models to simulate temporal scaling behavior represent stringent performance tests o...

We investigated the differences in brain fMRI signal complexity in patients with schizophrenia while performing the Cyberball social exclusion task, using measures of Sample entropy and Hurst exponent (H). 13 patients meeting diagnostic and Statistical Manual of Mental Disorders, 4th Edition (DSM IV) criteria for schizophrenia and 16 healthy controls underwent fMRI scanning at 1.5 T. The fMRI d...

We consider the class of pentagonal 3-polytopal graphs all of whose edges are incident either with two 3-valent vertices or with a 3-valent vertex and a q-valent vertex. For most values of q, (i) we find a small non-hamiltonian graph in the class and (ii) we show that the shortness exponent of the class and the shortness coefficient of a special subclass are less than one. For q--4, we find a p...

In this paper we establish the existence of path-wise solutions and the uniqueness in law for multidimensional stochastic differential equations driven by a multi-dimensional fractional Brownian motion with Hurst parameter H > 12 .

[1] The acquisition of new global elevation data from the Lunar Orbiter Laser Altimeter, carried on the Lunar Reconnaissance Orbiter, permits quantification of the surface roughness properties of the Moon at unprecedented scales and resolution. We map lunar surface roughness using a range of parameters: median absolute slope, both directional (along‐track) and bidirectional (in two dimensions);...

In this paper, we shed light on the dynamic characteristics of rational group behaviors and the relationship between monetary policy and economic units in the financial market by using an agent-based model (ABM), the Hurst exponent, and the Shannon entropy. First, an agent-based model is used to analyze the characteristics of the group behaviors at different levels of irrationality. Second, the...