Excursions Above the Minimum for Diffusions

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.]

This manuscript is available fromthe author upon request.
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May 13, 1998