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

   
@article{ECP1001,
	author = {Hiroyuki Matsumoto and Marc Yor},
	title = {Some Changes of Probabilities Related to a Geometric Brownian Motion Version of Pitman's $2M-X$ Theorem},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {4},
	year = {1999},
	keywords = {Diffusion Process, Geometric Brownian Motion, Markov Intertwining Kernel, (strict) Local Martingale, Explosion.},
	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.},
	pages = {no. 3, 15-23},
	issn = {1083-589X},
	doi = {10.1214/ECP.v4-1001},    
        url = {http://ecp.ejpecp.org/article/view/1001}}