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 Electronic Communications in Probability > Vol. 3 (1998) > Paper 10 open journal systems 


Brownian Excursion Conditioned on Its Local Time

David J. Aldous, University of California, Berkeley


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.


Full text: PDF

Pages: 79-90

Published on: September 22, 1998
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Electronic Communications in Probability. ISSN: 1083-589X