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First passage time distribution of a Wiener process with drift concerning two elastic barriers

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Marco Dominé
Marco Dominé*
Affiliation:
University of Magdeburg
*
∗Postal address: Department of Mathematical Stochastics, Otto-von-Guericke-University of Magdeburg, PSF 4120, 39016 Magdeburg, Germany.
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Abstract

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of elastic boundaries and a fixed start point. An explicit expression is obtained for the first passage density. The cases with pure absorbing and/or reflecting barriers arise for a special choice of a parameter constellation. These special cases are compared with results in Darling and Siegert [5] and Sweet and Hardin [15].

Keywords

FIRST PASSAGE TIMEFIRST EXIT TIMEELASTIC BOUNDARIESREFLECTIONABSORPTIONWIENER PROCESS

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60J65: Brownian motion 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 164 - 175
Copyright
Copyright © Applied Probability Trust 1996 

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