Levy-Brownian motion on finite intervals: Mean first passage time analysis

  • We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by Lévy stable noises. The complexity of the first passage time statistics (mean first passage time, cumulative first passage time distribution) is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non-Gaussian noises. The validity of the method is tested numerically and compared against analytical formulae when the stability index alpha approaches 2, recovering in this limit the standard results for the Fokker-Planck dynamics driven by Gaussian white noise.

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Author:Bartlomiej Dybiec, Ewa Gudowska Nowak, Peter HänggiORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/325
Publishing Institution:Universität Augsburg
Release Date:2006/08/31
Tag:Levy-Brownian motion; stochastic processes; noise
GND-Keyword:Brownsche Bewegung; Rauschen; Stochastischer Prozess
Source:erschienen in: Phys. Rev. E 73, 046104 (2006); DOI: 10.1103/PhysRevE.73.046104; URL: http://link.aps.org/abstract/PRE/v73/e046104
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik I
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik