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1998 Brownian Excursion Conditioned on Its Local Time
David Aldous
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Electron. Commun. Probab. 3: 79-90 (1998). DOI: 10.1214/ECP.v3-996

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.

Citation

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David Aldous. "Brownian Excursion Conditioned on Its Local Time." Electron. Commun. Probab. 3 79 - 90, 1998. https://doi.org/10.1214/ECP.v3-996

Information

Accepted: 22 September 1998; Published: 1998
First available in Project Euclid: 2 March 2016

zbMATH: 0914.60049
MathSciNet: MR1650567
Digital Object Identifier: 10.1214/ECP.v3-996

Subjects:
Primary: 60J55
Secondary: 60C05, 60J65

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