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.
Dubkov, A.A., La Cognata, A., Spagnolo, B. (2009). The problem of analytical calculation of barrier crossing characteristics for L´evy flights. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT, 2009-01-05 [10.1088/1742-5468/2009/01/P01002].
The problem of analytical calculation of barrier crossing characteristics for L´evy flights
LA COGNATA, Angelo;SPAGNOLO, Bernardo
2009-01-01
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.
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