Anomalous diffusion in systems driven by the stable Levy 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 generalised 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 Ito interpretation if the inertia is very large. An escape time from the potential well is calculated.

11 pages, 6 figures

References in corpus (3)

• Escape driven by $\alpha$-stable white noises
• Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media
• Anomalous diffusion for a correlated process with long jumps

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• Asymmetric Levy flights in nonhomogeneous environments
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• Inertial Lévy flights in bounded domains