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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Pages: 79-90

Publication Date: September 22, 1998

DOI: 10.1214/ECP.v3-996

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