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Moments of the first-passage time of a Wiener process with drift between two elastic barriers

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Marco Dominé
Marco Dominé*
Affiliation:
Otto-von-Guericke-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

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

Keywords

ELASTIC BOUNDARIESREFLECTIONABSORPTION

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 32 , Issue 4 , December 1995 , pp. 1007 - 1013
Copyright
Copyright © Applied Probability Trust 1995 

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References

[1] Ahlbehrendt, N. and Kempe, V. (1984) Analyse Stochastischer Systeme. Akademie-Verlag. Berlin.CrossRefGoogle Scholar
[2] Bharucha-Reid, A. T. (1960) Elements of the Theory of Markov Processes and Their Applications. McGraw-Hill, New York.Google Scholar
[3] Domine, M. (1996) First-passage time distribution of a Wiener process with drift concerning two elastic barriers. J. Appl. Prob. to appear.CrossRefGoogle Scholar
[4] Feller, W. (1952) The parabolic differential equations and the associated semigroups of transformations. Ann. Math. 55, 468–519.CrossRefGoogle Scholar