We examine possible closed form solutions for the cumulative distribution function for systems where the probability density function can be adequately described by the generalized non-extensive statistics framework. Application to financial time series as a possible Value at Risk technique...

We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The Rényi divergence appears as a natural by-product of the...

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-β) oscillator chains with different boundary conditions and numbers of...

We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index α3 and this index tends to increase quickly with decreasing sampling frequency. Our study is based on...

The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here, we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999–31.10.2005 for the...

Classical systems of coupled harmonic oscillators are studied using the Carati–Galgani model. We investigate the consequences for Einstein’s conjecture by considering that the exchange of energy in molecular collisions follows the Lévy type statistics. We develop a generalization of...

The inverse Mellin transform technique is utilized to obtain closed form representations of the generalized Boltzmann factors associated with several Weibull-type models such as the generalized gamma, Maxwell, Rayleigh and half-normal distributions. The results complement those already available...

Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the superstatistical model. Previously, the bistable Langevin model has...