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Some Changes of Probabilities Related to a Geometric Brownian Motion Version of Pitman's $2M-X$ Theorem

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1.	Title	Title of document	Some Changes of Probabilities Related to a Geometric Brownian Motion Version of Pitman's $2M-X$ Theorem
2.	Creator	Author's name, affiliation, country	Hiroyuki Matsumoto; Nagoya University
2.	Creator	Author's name, affiliation, country	Marc Yor; Universite Pierre et Marie Curie
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Diffusion Process, Geometric Brownian Motion, Markov Intertwining Kernel, (strict) Local Martingale, Explosion.
3.	Subject	Subject classification	60G44, 60J60.
4.	Description	Abstract	Rogers-Pitman have shown that the sum of the absolute value of $B^{(\mu)}$, Brownian motion with constant drift $\mu$, and its local time $L^{(\mu)}$ is a diffusion $R^{(\mu)}$. We exploit the intertwining relation between $B^{(\mu)}$ and $R^{(\mu)}$ to show that the same addition operation performed on a one-parameter family of diffusions ${X^{(\alpha,\mu)}}_{\alpha\in{\mathbf R}_+}$ yields the same diffusion $R^{(\mu)}$. Recently we obtained an exponential analogue of the Rogers-Pitman result. Here we exploit again the corresponding intertwining relationship to yield a one-parameter family extension of our result.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1999-06-03
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1001
10.	Identifier	Digital Object Identifier	10.1214/ECP.v4-1001
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 4
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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