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

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