A Semi-Markov Leaky Integrate-and-Fire Model

In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy...

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Bibliographic Details
Published in:	Mathematics (Basel) Vol. 7; no. 11; p. 1022
Main Authors:	Ascione, Giacomo, Toaldo, Bruno
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-11-2019
Subjects:	fractional equations Gaussian process lif models Markov analysis Markov processes Mathematics Noise Random variables semi-markov processes Stochastic models
Online Access:	Get full text
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Summary:	In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math7111022