Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

DY: Fachverband Dynamik und Statistische Physik

DY 30: Nonlinear stochastic systems

DY 30.2: Vortrag

Freitag, 27. März 2009, 10:30–10:45, ZEU 118

Properties of the Langevin equation driven by noises with heavy and super-heavy tailed distributions of the increments — •Stanislav Denisov¹, Peter Hänggi², and Holger Kantz¹ — ¹Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany — ²Institut für Physik, Universität Augsburg, D-86135 Augsburg, Germany

We present our results on the statistical properties of the solutions of the overdamped Langevin equation driven by noises whose increments are distributed with heavy and super-heavy tails. Starting from an arbitrary distribution of the increments, we derive the generalized Fokker-Planck equation that in a concise and natural way captures all known particular cases including the fractional Fokker-Planck equation associated with the Langevin equation driven by a Lévy stable noise [1]. We demonstrate that the fractional Fokker-Planck equation is valid also for all noises whose increments have heavy-tailed distributions and calculate its parameters in terms of the asymptotic characteristics of these distributions [2]. In the case of super-heavy tailed distributions of the noise increments, i.e., distributions that do not possess finite moments of any fractional order, the generalized Fokker-Planck equation is solved exactly and the role of these noises is analyzed.

[1] S.I. Denisov, W. Horsthemke, and P. Hänggi, Phys. Rev. E 77, 061112 (2008).

[2] S.I. Denisov, P. Hänggi, and H. Kantz, arXiv:0811.1162.