title: Lévy flights between absorbing boundaries: Revisiting the survival probability and the shift from the exponential to the Sparre-Andersen limit behavior.
abstract: We revisit the problem of calculating the survival probability of Lévy flights in a finite interval with absorbing boundaries. Our approach is based on the master equation for discrete Lévy fliers, previously considered to treat the semi-infinite domain. We argue that, although the semi-infinite case can be treated exactly due to Wiener-Hopf factorization, the approximation involved in the problem with the finite interval is actually fairly good. We evidence the shift in the universal behavior of the long-term survival probability from the exponential decay in the presence of two absorbing barriers to the Sparre-Andersen power-law dependence in the single-barrier limit. In some cases, we also calculate the short- and intermediate-term behavior and present the explicit dependence of the survival probability on the Lévy flier's starting position. Our analytical results are confirmed by numerical simulations.
authors.affiliation: Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife-PE, Brazil.
authors.forename: Hugo A
authors.initials: HA
authors.lastname: Araújo
authors.affiliation: Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife-PE, Brazil.
authors.forename: Ernesto P
authors.initials: EP
authors.lastname: Raposo