The problem of analytical calculation ofbarrier crossing characteristics for L´evyflights

By using the backward fractional Fokker–Planck equation weinvestigate the barrier crossing event in the presence of L´evy noise. Afterbriefly reviewing recent results obtained with different approaches on the timecharacteristics of the barrier crossing, we derive a general differential equationuseful to calculate the nonlinear relaxation time. We obtain analytically thenonlinear relaxation time for free L´evy flights and a closed expression inquadrature of the same characteristics for the cubic potential.