An integral equation for the distribution of the first exit time of a reflected Brownian motion

Victor De-la-Peña, Gerardo Hernandez-del-Valle, Carlos Gabriel Pacheco-Gonzalez


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.



Reflected Brownian motion, first passage time, Volterra integral equation


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.