On exit time of stable processes

2011/03/22 by Piotr Graczyk, Graczyk, Piotr, Tomasz Jakubowski +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G52 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1103.4251

openalex publication_date 2011/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the exit time τ=τ_(0,∞) for 1-dimensional strictly stable processes and express its Laplace transform at t^α as the Laplace transform of a positive random variable with explicit density. Consequently, τ satisfies some multiplicative convolution relations. For some stable processes, e.g. for the symmetric \frac23-stable process, explicit formulas for the Laplace transform and the density of τ are obtained as an application.

Citations

• The maximum of sums of stable random variables

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