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

Abstract

By using the backward fractional Fokker–Planck equation we
\ninvestigate the barrier crossing event in the presence of L ́evy noise. After
\nbriefly reviewing recent results obtained with different approaches on the time
\ncharacteristics of the barrier crossing, we derive a general differential equation
\nuseful to calculate the nonlinear relaxation time. We obtain analytically the
\nnonlinear relaxation time for free L ́evy flights and a closed expression in
\nquadrature of the same characteristics for the cubic potential.