Last-Hitting Times and Williams' Decomposition of the Bessel Process of Dimension 3 at its Ultimate Minimum

TL;DR

This paper discusses last-hitting times in optimal stopping theory and provides a concise proof of Williams' decomposition for the BES(3) process at its ultimate minimum, highlighting their importance in stochastic process analysis.

Contribution

It offers a new, concise proof of Williams' decomposition for BES(3), connecting last-hitting times with process decomposition at the ultimate minimum.

Findings

Concise proof of Williams' decomposition for BES(3)

Enhanced understanding of last-hitting times in stochastic processes

Link between last-hitting times and process decomposition

Abstract

In this note we shortly recall the importance of last-hitting times in theory and applications of optimal stopping. As a small contribution to this domain we then propose a concise proof of David Williams' decomposition of the Bessel Process of dimension 3 (BES(3)), starting from r > 0 at its ultimate minimum. This discussion is strongly motivated by our interest in properties of last hitting times in general, and here specifically, directly linked with the forthcoming reading guide of Nikeghbali and Platen on this subject.