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

F.T. Bruss , Marc Yor (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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

Domains: Probability [math.PR]

F.T. Bruss, Marc Yor. A New Proof of Williams' Decomposition of the Bessel Process of Dimension Three with a Look at Last-Hitting Times. Bulletin of the Belgian Mathematical Society - Simon Stevin, 2015, 22 (2), pp.319-330. ⟨10.36045/bbms/1432840867⟩. ⟨hal-01172500⟩