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2001 An analogue of Pitman's {$2M-X$} theorem for exponential Wiener functionals. II. The role of the generalized inverse Gaussian laws
Hiroyuki Matsumoto, Marc Yor
Nagoya Math. J. 162: 65-86 (2001).

Abstract

In Part I of this work, we have shown that the stochastic process $Z^{(\mu)}$ 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 $Z^{(\mu)}$ is intertwined with Brownian motion with drift $\mu$ and that the intertwining kernel may be expressed in terms of Generalized Inverse Gaussian laws.

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Hiroyuki Matsumoto. Marc Yor. "An analogue of Pitman's {$2M-X$} theorem for exponential Wiener functionals. II. The role of the generalized inverse Gaussian laws." Nagoya Math. J. 162 65 - 86, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 0983.60075
MathSciNet: MR1836133

Subjects:
Primary: 60J60
Secondary: 60J65

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

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