On the the successive passage times of certain one-dimensional diffusions

2018/03/27 by Mario Abundo, Abundo, Mario, Maria Beatrice Scioscia Santoro +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR

paper · pdf · doi:10.48550/arxiv.1803.09910

21 pages, 15 figures

openalex publication_date 2018/03/27 · arxiv created 2018/04/11 · arxiv updated 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the nth-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM, through a constant barrier a. Some explicit examples are reported.

Related

• Explicit Asymptotics on First Passage Times of Diffusion Processes
• Parisian times for linear diffusions
• The first passage time density of Brownian motion and the heat equation with Dirichlet boundary condition in time dependent domains
• First passage time properties of diffusion with a broad class of stochastic diffusion coefficients
• Exactly solvable diffusions from space-time transformations