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2013 | OriginalPaper | Chapter

Functionals of the Brownian Bridge

Author : Janosch Ortmann

Published in: Séminaire de Probabilités XLV

Publisher: Springer International Publishing

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Abstract

We discuss the distributions of three functionals of the free Brownian bridge: its L²-norm, the second component of its signature and its Lévy area. All of these are freely infinitely divisible. Two representations of the free Brownian bridge as series of free semicircular random variables are introduced and used. These are analogous to the Fourier representations of the classical Brownian bridge due to Lévy and Kac and the latter extends to all semicircular processes.

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Title: Functionals of the Brownian Bridge
Author: Janosch Ortmann
Publisher: Springer International Publishing
Book: Séminaire de Probabilités XLV
Print ISBN: 978-3-319-00320-7

Electronic ISBN: 978-3-319-00321-4

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-3-319-00321-4_17