The problem of analytical calculation of barrier crossing characteristics for Levy flights

Abstract

By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Levy noise. After shortly review recent results obtained with different approaches on the time characteristics of the barrier crossing, we derive a general differential equation useful to calculate the nonlinear relaxation time. We obtain analytically the nonlinear relaxation time for free Levy flights and a closed expression in quadrature of the same characteristics for cubic potential.

12 pages, 2 figures, presented at 5th International Conference on Unsolved Problems on Noise, Lyon, France, 2008, to appear in J. Stat. Mech.: Theory and Experiment

References in corpus (3)

• Escape driven by $\alpha$-stable white noises
• First exit times for Lévy-driven diffusions with exponentially light jumps
• Comment on "Mean First Passage Time for Anomalous Diffusion"