Electronic Communications in Probability

Brownian Excursion Conditioned on Its Local Time

David Aldous

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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.

Article information

Electron. Commun. Probab., Volume 3 (1998), paper no. 10, 79-90.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J55: Local time and additive functionals
Secondary: 60J65: Brownian motion [See also 58J65] 60C05: Combinatorial probability

Brownian excursion continuum random tree Kingman's coalescent local time

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Aldous, David. Brownian Excursion Conditioned on Its Local Time. Electron. Commun. Probab. 3 (1998), paper no. 10, 79--90. doi:10.1214/ECP.v3-996. https://projecteuclid.org/euclid.ecp/1456935916

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