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AN INTEGRAL EQUATION FOR THE DISTRIBUTION OF THE FIRST EXIT TIME OF A REFLECTED BROWNIAN MOTION

Part of: Numerical approximation and computational geometry Stochastic processes Volterra integral equations

Published online by Cambridge University Press:  04 December 2009

VICTOR DE-LA-PEÑA ,
GERARDO HERNÁNDEZ-DEL-VALLE  and
CARLOS G. PACHECO-GONZÁLEZ
VICTOR DE-LA-PEÑA*
Affiliation:
Statistics Department, Columbia University, 1255 Amsterdam Ave. Mail Code 4403, New York, NY, USA (email: vp@stat.columbia.edu)
GERARDO HERNÁNDEZ-DEL-VALLE
Affiliation:
Statistics Department, Columbia University, USA (email: gerardo@stat.columbia.edu)
CARLOS G. PACHECO-GONZÁLEZ
Affiliation:
Departamento de Matematicas, CINVESTAV-IPN, A. Postal 14-740, Mexico D.F. 07000, Mexico, USA (email: cpacheco@math.cinvestav.mx)
*
✉For correspondence; e-mail: vp@stat.columbia.edu
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Abstract

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Reflected Brownian motion is used in areas such as physiology, electrochemistry and nuclear magnetic resonance. We study the first-passage-time problem of this process which is relevant in applications; specifically, we find a Volterra integral equation for the distribution of the first time that a reflected Brownian motion reaches a nondecreasing barrier. Additionally, we note how a numerical procedure can be used to solve the integral equation.

Keywords

reflected Brownian motionfirst passage timeVolterra integral equation

MSC classification

Secondary: 60G07: General theory of processes 45D05: Volterra integral equations 65D15: Algorithms for functional approximation
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 4 , April 2009 , pp. 445 - 454
Copyright
Copyright © Australian Mathematical Society 2009

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