Excursions Above the Minimum for Diffusions

2013/08/23 by P. J. Fitzsimmons, Fitzsimmons, P. J.
Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1308.5189

openalex publication_date 2013/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate the existence of a "Lévy system" for the excursions of a one-dimensional diffusion process above its past-minimum process. As applications we provide a direct proof of D. Williams' decomposition (in both a global and a local form) and of a theorem of W. Vervaat.

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