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The Brownian excursion multi-dimensional local time density

Part of: Markov processes Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Bernhard Gittenberger  and
Guy Louchard
Bernhard Gittenberger*
Affiliation:
Technische Universitat Wien
Guy Louchard*
Affiliation:
Université Libre de Bruxelles
*
∗Postal address: Department of Geometry, TU Wien, Wiedner Hauptstraße 8–10/113, A-1040 Wien, Austria. Email address: gittenberger@tuwien.ac.at
∗∗Postal address: Université Libre de Bruxelles, Département d'Informatique C.P. 212, Campus de la Plaine, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
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Abstract

Expressions for the multi-dimensional densities of Brownian excursion local time are derived by two different methods: a direct method based on Kac's formula for Brownian functionals and an indirect one based on a limit theorem for Galton–Watson trees.

Keywords

Brownian excursionlocal timerandom trees

MSC classification

Primary: 60J55: Local time and additive functionals
Secondary: 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 350 - 373
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

This author's work was supported by the Austrian Science Foundation FWF, grant P10187-PHY.

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