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

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

2005-12-20

arxiv.org/abs/cond-mat/0512492v2

Physics

Condensed Matter

Statistical Mechanics

9 pages, 13 figures

Scientific paper

10.1103/PhysRevE.73.046104

We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by L\'evy 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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