L\'{e}vy flights as subordination process: first passage times

TL;DR

This paper derives the first passage time density for Lévy flights using a subordination approach, linking Brownian motion and Sparre Andersen theorem, and extends results to broader waiting time distributions.

Contribution

It introduces a subordination-based method to obtain first passage times for Lévy flights, bypassing fractional diffusion equations and generalizing previous results.

Findings

First passage time density derived from subordination scheme

Asymptotic behavior inferred from Brownian solution and Sparre Andersen theorem

Results extend to broad waiting time distributions

Abstract

We obtain the first passage time density for a L\'{e}vy flight random process from a subordination scheme. By this method, we infer the asymptotic behavior directly from the Brownian solution and the Sparre Andersen theorem, avoiding explicit reference to the fractional diffusion equation. Our results corroborate recent findings for Markovian L\'{e}vy flights and generalize to broad waiting times.