A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model
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Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli
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Istituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, Napoli
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Received:
01 December 2012
Accepted:
29 June 2018
Published:
01 September 2013
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MSC :
Primary: 60J60; Secondary: 60H35.
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A method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. The proposed procedure is particularly efficient in the case of the Ornstein-Uhlenbeck process, which is important for modeling spiking neuronal activity.
Citation: Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model[J]. Mathematical Biosciences and Engineering, 2014, 11(1): 1-10. doi: 10.3934/mbe.2014.11.1
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Abstract
A method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. The proposed procedure is particularly efficient in the case of the Ornstein-Uhlenbeck process, which is important for modeling spiking neuronal activity.
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