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.
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