English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We discuss the first passage time problem in the semi-infinite interval, forhomogeneous stochastic Markov processes with L{\'e}vy stable jump lengthdistributions $\lambda(x)\sim\ell^{\alpha}/|x|^{1+\alpha}$ ($|x|\gg\ell$),namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the methodof images leads to a result, which violates a theorem due to Sparre Andersen,according to which an arbitrary continuous and symmetric jump lengthdistribution produces a first passage time density (FPTD) governed by theuniversal long-time decay $\sim t^{-3/2}$. Conversely, we show that for LFs thedirect definition known from Gaussian processes in fact defines the probabilitydensity of first arrival, which for LFs differs from the FPTD. Our findings arecorroborated by numerical results.Comment: 8 pages, 3 figures, iopart.cls style, accepted to J. Phys. A (Lett

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