Excursions Above the Minimum for Diffusions

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.

This manuscript was written in the spring of 1985, but has never been submitted for publication

Cited by in corpus (3)

• Poisson ensembles of loops of one-dimensional diffusions
• The Vervaat transform of Brownian bridges and Brownian motion
• Some asymptotic formulae for Bessel process