Statistics of residence time for Lévy flights in unstable parabolic potentials.

Dubkov, Alexander A; Dybiec, Bartłomiej; Spagnolo, Bernardo; Kharcheva, Anna; Guarcello, Claudio; Valenti, Davide · Phys Rev E · 2020

basic_science · Level V

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Abstract

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.