Hitting densities for spectrally positive stable processes

2010/02/08 by Thomas Simon, Simon, Thomas
Economics, Econometrics and Finance · Mathematics · #60E05 #60G52 #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1002.1540

openalex publication_date 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A multiplicative identity in law connecting the hitting times of completely asymmetric α-stable Lévy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute fractional moments and to get series representations for the density. We also prove that the hitting times are unimodal as soon as α≤ 3/2. Analogous results are obtained, in a much simplified manner, for the first passage time across a positive level.

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