First passage and arrival time densities for Lévy flights and the failure of the method of images

DOI10.1088/0305-4470/36/41/L01zbMATH Open1049.60090arXivcond-mat/0309449OpenAlexW2025673572MaRDI QIDQ4468569

Author name not available (Why is that?)

Publication date: 10 June 2004

Published in: (Search for Journal in Brave)

Abstract: We discuss the first passage time problem in the semi-infinite interval, for homogeneous stochastic Markov processes with L{'e}vy stable jump length distributions $lambda(x)simel{l}^{alpha}/|x{|}^{1+alpha}$ ($|x|ggell$), namely, L{'e}vy flights (LFs). In particular, we demonstrate that the method of images leads to a result, which violates a theorem due to Sparre Andersen, according to which an arbitrary continuous and symmetric jump length distribution produces a first passage time density (FPTD) governed by the universal long-time decay $sim{t}^{-3/2}$. Conversely, we show that for LFs the direct definition known from Gaussian processes in fact defines the probability density of first arrival, which for LFs differs from the FPTD. Our findings are corroborated by numerical results.

Full work available at URL: https://arxiv.org/abs/cond-mat/0309449

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: First passage and arrival time densities for Lévy flights and the failure of the method of images

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4468569)