A stochastic model for the firing activity of a neuronal unit has been recently proposed in Di Crescenzo and Martinucci (2007). It includes the decay effect of the membrane potential in the absence of stimuli, and the occurrence of excitatory inputs driven by a Poisson process. In order to add the effects of inhibitory stimuli, we now propose a Stein-type model based on a suitable exponential transformation of a bilateral birth-death process on ${\mathbb Z}$ and characterized by state-dependent nonlinear birth and death rates. We perform an analysis of the probability distribution of the stochastic process describing the membrane potential and make use of a simulation-based approach to obtain some results on the firing density.

A neuronal model with excitatory and inhibitory inputs governed by a birth-death process

DI CRESCENZO, Antonio;MARTINUCCI, BARBARA
2009-01-01

Abstract

A stochastic model for the firing activity of a neuronal unit has been recently proposed in Di Crescenzo and Martinucci (2007). It includes the decay effect of the membrane potential in the absence of stimuli, and the occurrence of excitatory inputs driven by a Poisson process. In order to add the effects of inhibitory stimuli, we now propose a Stein-type model based on a suitable exponential transformation of a bilateral birth-death process on ${\mathbb Z}$ and characterized by state-dependent nonlinear birth and death rates. We perform an analysis of the probability distribution of the stochastic process describing the membrane potential and make use of a simulation-based approach to obtain some results on the firing density.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/2500904
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