Recognition of stable distribution with Lévy index α close to 2.

We address the problem of recognizing α-stable Lévy distribution with Lévy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution is not clearly detectable, and the shape of the empirical probability density function is close to a Gaussian. We propose a testing procedure combining a simple visual test based on empirical fourth moment with the Anderson-Darling and Jarque-Bera statistical tests and we check the efficiency of the method on simulated data.

Kramers-like escape driven by fractional Gaussian noise.

We investigate the escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0 View Article and Find Full Text PDF

Fractal properties of anomalous diffusion in intermittent maps.

An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random-walk theory well approximates the coarse behavior of this quantity in terms of a continuous function.

Natural cutoff in Lévy flights caused by dissipative nonlinearity.

Lévy flight models are often used to describe stochastic processes in complex systems. However, due to the occurrence of diverging position and/or velocity fluctuations Lévy flights are physically problematic if describing the dynamics of a particle of finite mass. Here we show that the velocity distribution of a random walker subject to Lévy noise can be regularized by nonlinear friction, leading to a natural cutoff in the velocity distribution and finite velocity variance.

Bifurcation, bimodality, and finite variance in confined Lévy flights.

We investigate the statistical behavior of Lévy flights confined in a symmetric, quartic potential well U(x) proportional, variant x(4). At stationarity, the probability density function features a distinct bimodal shape and decays with power-law tails which are steep enough to give rise to a finite variance, in contrast to free Lévy flights. From a delta-initial condition, a bifurcation of the unimodal state is observed at t(c)>0.