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Path transformations of first passage bridges

   
@article{ECP1096,
	author = {Jean Bertoin and Loic Chaumont and Jim Pitman},
	title = {Path transformations of first passage bridges},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {8},
	year = {2003},
	keywords = {},
	abstract = {We define the first passage bridge from 0 to $\lambda$ as the Brownian motion on the time interval $[0,1]$ conditioned to first hit $\lambda$ at time 1. We show that this process may be related to the Brownian bridge, the Bessel bridge or the Brownian excursion via some path transformations, the main one being an extension of Vervaat's transformation. We also propose  an extension of these results to certain bridges with cyclically exchangeable increments.},
	pages = {no. 17, 155-166},
	issn = {1083-589X},
	doi = {10.1214/ECP.v8-1096},    
        url = {http://ecp.ejpecp.org/article/view/1096}}