On the Moments of Firing Numbers in Diffusion Neuronal Models with Refractoriness

Giorno, Virginia; Nobile, Amelia Giuseppina; Ricciardi, Luigi M.

doi:10.1007/11499220_20

Cited by 3 publications

(2 citation statements)

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“…[72]) upon the nature of the lower boundary in x = 0 for the process (50) or in x = V I for the process (47) and on the selected boundary condition for the solution of its Kolmogorov equation. If we impose a zero-flux condition (49) in the origin, using the notation (51), we obtain the transition pdf (cf. [44]):…”

Section: Reversal Potential Modelsmentioning

confidence: 99%

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Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications

Sacerdote

Giraudo

2012

Lecture Notes in Mathematics

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Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved and numerical and simulation methods have been developed for their study. Reviews appeared recently collect the main features of these models but do not focus on the methodologies employed to obtain them. Aim of this paper is to fill this gap by upgrading old reviews on this topic. The idea is to collect the existing methods and the available analytical results for the most common one dimensional stochastic Integrate and Fire models to make them available for studies on networks. An effort to unify the mathematical notations is also made. This review is divided in two parts:1. Derivation of the models with the list of the available closed forms expressions for their characterization; 2. Presentation of the existing mathematical and statistical methods for the study of these models.

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Section: Reversal Potential Modelsmentioning

confidence: 99%

“…If the first three moments of the refractory period are finite, the following asymptotic expressions for large times hold for the first two moments of M (cf. [49]):…”

Section: Refractoriness and Return Process Modelsmentioning

confidence: 99%