title: Anomalous diffusion in systems driven by the stable Lévy noise with a finite noise relaxation time and inertia.
abstract: Dynamical systems driven by a general Lévy stable noise are considered. The inertia is included and the noise, represented by a generalized Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive noise) is solved: the resulting distribution converges with time to the distribution for the white-noise, massless case. Moreover, a multiplicative noise is discussed. It can make the distribution steeper and the variance, which is finite, depends sublinearly on time (subdiffusion). For a small mass, a white-noise limit corresponds to the Stratonovich interpretation. On the other hand, the distribution tails agree with the Itô interpretation if the inertia is very large. An escape time from the potential well is calculated.
authors.affiliation: Institute of Nuclear Physics, Polish Academy of Sciences, PL-31-342 Kraków, Poland.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Srokowski
mesh_terms: D000054:Acceleration; D003198:Computer Simulation; D004058:Diffusion; D016014:Linear Models