The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model

Aniello Buonocore (), Luigia Caputo (), Enrica Pirozzi () and Luigi M. Ricciardi ()
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Aniello Buonocore: Università di Napoli Federico II
Luigia Caputo: Università di Torino
Enrica Pirozzi: Università di Napoli Federico II
Luigi M. Ricciardi: Università di Napoli Federico II

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 1, 29-57

Abstract: Abstract Motivated by some unsolved problems of biological interest, such as the description of firing probability densities for Leaky Integrate-and-Fire neuronal models, we consider the first-passage-time problem for Gauss-diffusion processes along the line of Mehr and McFadden (J R Stat Soc B 27:505–522, 1965). This is essentially based on a space-time transformation, originally due to Doob (Ann Math Stat 20:393–403, 1949), by which any Gauss-Markov process can expressed in terms of the standard Wiener process. Starting with an analysis that pinpoints certain properties of mean and autocovariance of a Gauss-Markov process, we are led to the formulation of some numerical and time-asymptotically analytical methods for evaluating first-passage-time probability density functions for Gauss-diffusion processes. Implementations for neuronal models under various parameter choices of biological significance confirm the expected excellent accuracy of our methods.

Keywords: Gaussian process; Diffusion; LIF neuronal models; Numerical approximations; Asymptotics; 02.50Ey; 02.50.Ga; 02.60.Jh; 60J60; 60J70; 6015; 92C20; 60J60; 60G15; 60J70 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11009-009-9132-8

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