Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion

Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion.

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Tempered fractional Brownian motion

Brownian motion exhibiting absolute negative mobility.

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for F>0 and positive for F<0 (absolute negative mobility).

The Model of Real Data Constructing Using Fractional Brownian Motion

Let’s assume , ,.., 1 , n k t t k = = , 0 , 0 ) 1 ( 1 1 = − − + = t n T k t tk ) ))( ( ( k k t X x ⋅ Φ = is a model of observed time series . ... 1 n x x Let’s call ξ as a basic process of the model. Levy processes with independent stationary increments have been considered as basic for models of time series (particularly financial) [1-4]. The next step in the development of the models is trans...