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First Passage Time of Skew Brownian Motion

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  04 February 2016

Thilanka Appuhamillage  and
Daniel Sheldon
Thilanka Appuhamillage*
Affiliation:
Oregon State University
Daniel Sheldon*
Affiliation:
Oregon State University
*
∗ Postal address: Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA. Email address: ireshara@math.oregonstate.edu
∗∗ Postal address: School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331, USA. Email address: sheldon@eecs.oregonstate.edu
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Abstract

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Nearly fifty years after the introduction of skew Brownian motion by Itô and McKean (1963), the first passage time distribution remains unknown. In this paper we first generalize results of Pitman and Yor (2011) and Csáki and Hu (2004) to derive formulae for the distribution of ranked excursion heights of skew Brownian motion, and then use these results to derive the first passage time distribution.

Keywords

Skew Brownian motionranked excursion heightfirst passage time

MSC classification

Primary: 60G99: None of the above, but in this section
Secondary: 60H99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 685 - 696
Copyright
© Applied Probability Trust 

Footnotes

Research supported in part by the grant CMG EAR0724865 from the National Science Foundation.

Research supported in part by the grant DBI-0905885 from the National Science Foundation.

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