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An Analogue of Pitman’s 2M — X Theorem for Exponential Wiener Functionals Part II: The Role of the Generalized Inverse Gaussian Laws

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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In Part I of this work, we have shown that the stochastic process Z(µ) defined by (8.1) below is a diffusion process, which may be considered as an extension of Pitman’s 2M — X theorem. In this Part II, we deduce from an identity in law partly due to Dufresne that Z(µ) is intertwined with Brownian motion with drift µ and that the intertwining kernel may be expressed in terms of Generalized Inverse Gaussian laws.

Keywords

60J60
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 162 , June 2001 , pp. 65 - 86
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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