Dresden 2014 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Nonlinear Stochastic Systems

DY 10.8: Vortrag

Dienstag, 1. April 2014, 11:30–11:45, ZEU 160

1/f noise from nonlinear stochastic differential equations driven by Lévy noise. — •Rytis Kazakevičius and Julius Ruseckas — Institute of Theoretical Physics and Astronomy, Vilnius University, A. Gostauto 12, LT-01108 Vilnius, Lithuania

The Lévy process constitute the most general class of stable processes while the Gaussian process is their special case. The physical reason behind the Lévy non-Gaussian processes traces back to the nonhomogeneous structure of the environment, in particular, fractal or multi-fractal [1]. A class of nonlinear stochastic differential equations providing the power-law behavior of spectra, including 1/f noise, and the power-law distributions of the probability density has been proposed [2]. Usually such equations are driven by white Gaussian noise. We have generalized the nonlinear stochastic differential equations to be driven by Lévy noise instead of Gaussian noise. To preserve statistical properties of the generated signal we have changed the drift term in the equations. We have analyzed two cases when the signal is positive and when the signal can also be negative. In contrast to the equation with the Gaussian noise, the constant in the drift term is different in those two cases.

[1] T. Srokowski, Phys. Rev E 78, 031135 (2008).

[2] B. Kaulakys, J. Ruseckas, V. Gontis and M. Alaburda, Physica A 365, 217 (2006).