Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-30T08:51:06.459Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Stochastic processes Markov 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.
Get access Rights & Permissions [Opens in a new window]

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.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1007 - 1013
Copyright
Copyright © Applied Probability Trust 1995 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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