Eur. Phys. J. Special Topics 216, 31-35 (2013)
https://doi.org/10.1140/epjst/e2013-01726-2

Regular Article

Time characteristics of Lévy flights in a steep potential well

¹ Lobachevsky State University, Radiophysics Faculty, 23 Gagarin Ave., 603950 Nizhni Novgorod, Russia
² Università di Palermo, Dipartimento di Fisica, Group of Interdisciplinary Physics and CNISM, Viale delle Scienze, ed. 18, 90128 Palermo, Italy

^a e-mail: dubkov@rf.unn.ru

Received: 30 November 2012
Revised: 6 December 2012
Published online: 31 January 2013

Abstract

Using the method previously developed for ordinary Brownian diffusion, we derive a new formula to calculate the correlation time of stationary Lévy flights in a steep potential well. For the symmetric quartic potential, we obtain the exact expression of the correlation time of steady-state Lévy flights with index α = 1. The correlation time of stationary Lévy flights decreases with an increasing noise intensity and steepness of potential well.