Abstract
A stochastic model for the firing activity of a neuronal unit has been recently proposed in [4]. 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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Di Crescenzo, A., Martinucci, B. (2009). A Neuronal Model with Excitatory and Inhibitory Inputs Governed by a Birth-Death Process. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory - EUROCAST 2009. EUROCAST 2009. Lecture Notes in Computer Science, vol 5717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04772-5_17
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DOI: https://doi.org/10.1007/978-3-642-04772-5_17
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