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

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

Content Provider	Springer Nature Link
Author	Caputo, Luigia Pirozzi, Enrica Ricciardi, Luigi M. Buocore, Aniello
Copyright Year	2009
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.
Ending Page	57
Page Count	29
Starting Page	29
File Format	PDF
ISSN	13875841
e-ISSN	15737713
Journal	Methodology and Computing in Applied Probability
Issue Number	1
Volume Number	13
Language	English
Publisher	Springer US
Publisher Date	2009-05-05
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Economics general Diffusion processes Business/Management Science Asymptotics Statistics LIF neuronal models Numerical approximations Life Sciences Gaussian process Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) Diffusion Neural biology Electrical Engineering
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability

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