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Brownian Excursion Conditioned on Its Local Time

   
@article{ECP996,
	author = {David Aldous},
	title = {Brownian Excursion Conditioned on Its Local Time},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {3},
	year = {1998},
	keywords = {Brownian excursion,  continuum random tree, Kingman's coalescent, local time.},
	abstract = {For a function $\ell$ satisfying suitable integrability (but not continuity) requirements, we construct a process $(B^\ell_u, 0 \leq u \leq 1)$ interpretable as Brownian excursion conditioned to have local time $\ell(\cdot)$ at time $1$. The construction is achieved by first defining a non-homogeneous version of Kingman's coalescent and then applying the general theory in Aldous (1993) relating excursion-type processes to continuum random trees. This complements work of Warren and Yor (1997) on the Brownian burglar.},
	pages = {no. 10, 79-90},
	issn = {1083-589X},
	doi = {10.1214/ECP.v3-996},    
        url = {http://ecp.ejpecp.org/article/view/996}}