Electronic Communications in Probability

Brownian Excursion Conditioned on Its Local Time

David Aldous

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456935916

Digital Object Identifier
doi:10.1214/ECP.v3-996

Mathematical Reviews number (MathSciNet)
MR1650567

Zentralblatt MATH identifier
0914.60049

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

Keywords
Brownian excursion continuum random tree Kingman's coalescent local time

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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References

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