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On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes

A Semi-Markov Leaky Integrate-and-Fire Model

by 1,*,† and 2,†
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, I-80126 Naples, Italy
Dipartimento di Matematica “Giuseppe Peano”, Università degli Studi di Torino, 10123 Torino, Italy
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(11), 1022;
Received: 9 September 2019 / Revised: 22 October 2019 / Accepted: 24 October 2019 / Published: 29 October 2019
(This article belongs to the Special Issue Stochastic Processes in Neuronal Modeling)
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. View Full-Text
Keywords: Semi-Markov processes; LIF models; fractional equations Semi-Markov processes; LIF models; fractional equations
MDPI and ACS Style

Ascione, G.; Toaldo, B. A Semi-Markov Leaky Integrate-and-Fire Model. Mathematics 2019, 7, 1022.

AMA Style

Ascione G, Toaldo B. A Semi-Markov Leaky Integrate-and-Fire Model. Mathematics. 2019; 7(11):1022.

Chicago/Turabian Style

Ascione, Giacomo, and Bruno Toaldo. 2019. "A Semi-Markov Leaky Integrate-and-Fire Model" Mathematics 7, no. 11: 1022.

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