A first passage problem for a bivariate diffusion process: Numerical solution with an application to neuroscience when the process is Gauss-Markov

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• 作者：Elisa Benedetto ^{elisa.benedetto@unito.it} ; Laura Sacerdote ^{laura.sacerdote@unito.it} ; Cristina Zucca ; ^{cristina.zucca@unito.it}
• 关键词：First passage time ; Bivariate diffusion ; Integrated Brownian motion ; Integrated Ornstein&ndash ; Uhlenbeck process ; Two-compartment neuronal model
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2013
• 出版时间：April, 2013
• 年：2013
• 卷：242
• 期：Complete
• 页码：41-52
• 全文大小：299 K

文摘

We consider a bivariate Gauss-Markov process and we study the first passage time of one component through a constant boundary. We prove that its probability density function is the unique solution of a new integral equation and we propose a numerical algorithm for its solution. Convergence properties of this algorithm are discussed and the method is applied to the study of the integrated Brownian motion and to the integrated Ornstein-Uhlenbeck process. Finally a model of neuroscience interest is discussed.