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

F. Thomas Bruss and Marc Yor

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1432840867

Mathematical Reviews number (MathSciNet)
MR3351045

Zentralblatt MATH identifier
1329.60275

Subjects
Primary: 60 H 30
Secondary: 60 G 40

Keywords
Brownian motion Ornstein-Uhlenbeck process stopping times measurability $1/e$-law of best choice last arrival problem proportional increment process compassionate-use clinical trials

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


Export citation