## Bulletin of the Belgian Mathematical Society - Simon Stevin

### A New Proof of Williams' Decomposition of the Bessel Process of Dimension Three with a Look at Last-Hitting Times

#### Abstract

In this note we 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. An ultimate minimum of a stochastic process may be seen as a state of a process at a last hitting time. This discussion is strongly motivated by our interest in properties of last hitting times in general, and here specifically, directly linked with the reading guide of Nikeghbali and Platen (2013).

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 2 (2015), 319-330.

Dates
First available in Project Euclid: 28 May 2015

https://projecteuclid.org/euclid.bbms/1432840867

Digital Object Identifier
doi:10.36045/bbms/1432840867

Mathematical Reviews number (MathSciNet)
MR3351045

Zentralblatt MATH identifier
1329.60275

Subjects
Primary: 60 H 30
Secondary: 60 G 40

#### Citation

Bruss, F. Thomas; Yor, Marc. A New Proof of Williams' Decomposition of the Bessel Process of Dimension Three with a Look at Last-Hitting Times. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 319--330. doi:10.36045/bbms/1432840867. https://projecteuclid.org/euclid.bbms/1432840867