Statistics of residence time for Lévy flights in unstable parabolic potentials

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Statistics of residence time for Lévy flights in unstable parabolic potentials

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2020. Vol. 102. P. 042142.

Kharcheva A. A., Dubkov A. A., Spagnolo B., Dybiec B., Guarcello C., Valenti D.

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.

Language: English

DOI

Text on another site

Keywords: Levy noise

Strong solutions to stochastic equations with a Lévy noise and a non-constant diffusion coefficient

Bogachev V., Pilipenko A. Y., Doklady Mathematics 2016 Vol. 94 No. 1 P. 438–440

The goal of this study is to prove an existence and uniqueness theorem for the solution of a stochastic differential equation with Lévy noise in the case where the drift coefficient can be discontinuous. Additionally, the differentiability of the solution with respect to the initial condition is proved. ...

Added: November 16, 2016