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An analogue of Pitman’s 2M – X theorem for exponential Wiener functionals: Part I: A time-inversion approach

Published online by Cambridge University Press:  22 January 2016

Hiroyuki Matsumoto  and
Marc Yor
Hiroyuki Matsumoto
Affiliation:
School of Informatics and Sciences, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan, FAX: 052-789-4800, matsu@info.human.nagoya-u.ac.jp
Marc Yor
Affiliation:
Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, Place Jussieu, Tour 56, F-75252 Paris Cedex 05, France, FAX: +33 1 44 27 72 23
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Abstract

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Let be a one-dimensional Brownian motion with constant drift µ ∈ R starting from 0. In this paper we show that

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 and, in particular, its relation to the generalized Bessel processes.

Keywords

60J60
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 159 , 2000 , pp. 125 - 166
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

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