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2015 | OriginalPaper | Buchkapitel

Patterns in Random Walks and Brownian Motion

verfasst von : Jim Pitman, Wenpin Tang

Erschienen in: In Memoriam Marc Yor - Séminaire de Probabilités XLVII

Verlag: Springer International Publishing

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Abstract

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.

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Titel: Patterns in Random Walks and Brownian Motion
verfasst von: Jim Pitman
Wenpin Tang
Verlag: Springer International Publishing
Buch: In Memoriam Marc Yor - Séminaire de Probabilités XLVII
Print ISBN: 978-3-319-18584-2

Electronic ISBN: 978-3-319-18585-9

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-18585-9_4