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

• Autores: Elisa Benedetto, Laura Sacerdote, Cristina Zucca
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 242, Nº 1, 2013, págs. 41-52
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.10.014
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• Resumen

  • 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.