P. J. Fitzsimmons
Published 2013-08-23Version 1
We demonstrate the existence of a "L\'evy 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.
Comments: This manuscript was written in the spring of 1985, but has never been submitted for publication
Convergences of looptrees coded by excursions
Uniform convergence of conditional distributions for one-dimensional diffusion processes
Excursions of diffusion processes and continued fractions
![QR code for arXiv:1308.5189 [math.PR]](http://oss.arxitics.com/images/favicon.svg)