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

• Autores: Víctor de la Peña, Gerardo Hernández del Valle, Carlos G. Pacheco González
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 50, Nº 4, 2009, págs. 445-454
• Idioma: inglés
• DOI: 10.1017/s144618110900025x
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• Resumen

  • 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.