Nagoya Mathematical Journal

An analogue of Pitman's {$2M-X$} theorem for exponential Wiener functionals. II. The role of the generalized inverse Gaussian laws

Hiroyuki Matsumoto and Marc Yor

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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.

Article information

Source
Nagoya Math. J., Volume 162 (2001), 65-86.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631591

Mathematical Reviews number (MathSciNet)
MR1836133

Zentralblatt MATH identifier
0983.60075

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J65: Brownian motion [See also 58J65]

Citation

Matsumoto, Hiroyuki; Yor, Marc. 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 (2001), 65--86. https://projecteuclid.org/euclid.nmj/1114631591


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