The problem of analytical calculation of barrier crossing characteristics for L´evy flights
- Authors: Dubkov, AA; La Cognata, A; Spagnolo, B
- Publication year: 2009
- Type: Articolo in rivista (Articolo in rivista)
- Key words: exact results, stochastic particle dynamics (theory)
- OA Link: http://hdl.handle.net/10447/40919
Abstract
By using the backward fractional Fokker–Planck equation we investigate the barrier crossing event in the presence of L´evy noise. After briefly reviewing 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 L´evy flights and a closed expression in quadrature of the same characteristics for the cubic potential.