Statistics of Residence Time for Lévy Flights in Unstable Parabolic Potentials


We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones. o̧pyright 2020 American Physical Society.

Physical Review E
Davide Valenti
Davide Valenti
Full Professor