Translator Disclaimer
2000 An analogue of Pitman's $2M-X$theorem for exponential Wiener functionals. I. A time-inversion approach
Hiroyuki Matsumoto, Marc Yor
Nagoya Math. J. 159: 125-166 (2000).

Abstract

Let $\{B_t^{(\mu)},t\geqq0\}$ be a one-dimensional Brownian motion with constant drift $\mu\in{\bf R}$ starting from $0$. In this paper we show that $$ Z_t^{(\mu)} = \exp(-B_t^{(\mu)}) \int_0^t \exp(2B_s^{(\mu)}) ds $$ gives rise to a diffusion process and we explain how this result may be considered as an extension of the celebrated Pitman's $2M-X$ theorem. We also derive the infinitesimal generator and some properties of the diffusion process $\{Z_t^{(\mu)},t\geqq0\}$ and, in particular, its relation to the generalized Bessel processes.

Citation

Download Citation

Hiroyuki Matsumoto. Marc Yor. "An analogue of Pitman's $2M-X$theorem for exponential Wiener functionals. I. A time-inversion approach." Nagoya Math. J. 159 125 - 166, 2000.

Information

Published: 2000
First available in Project Euclid: 27 April 2005

zbMATH: 0963.60076
MathSciNet: MR1783567

Subjects:
Primary: 60J60
Secondary: 60J65

Rights: Copyright © 2000 Editorial Board, Nagoya Mathematical Journal

JOURNAL ARTICLE
42 PAGES


SHARE
Vol.159 • 2000
Back to Top