Power-law statistics from nonlinear stochastic differential equations driven by Lévy stable noise

摘要: Anomalous diffusion occurring in complex dynamical systems can often be described by Langevin equations driven Levy stable noise. Nonlinear stochastic differential yielding power-law steady state distribution and generating signals with 1/f power spectral density generalized replacing the Gaussian noise a more general These nonlinear generate exhibiting anomalous diffusion: either sub-diffusion or super-diffusion. In special case when stability index is α=2, we retain We investigate numerically frequency range where spectrum has form demonstrate that this depends on exponent as well of α. expect generalization may useful for describing fluctuations diffusion.