Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models

A. Buonocore, L. Caputo, A.G. Nobile and E. Pirozzi

Applied Mathematics and Computation, 2014, vol. 232, issue C, 799-809

Abstract: Gauss–Markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined. Furthermore, the first-passage time density through a time-dependent threshold is studied by using analytical, numerical and asymptotic methods. The restricted Gauss–Markov processes are then used to construct inhomogeneous leaky integrate-and-fire stochastic models for single neurons activity in the presence of a reversal hyperpolarization potential and time-varying input signals.

Keywords: Integrate-and-fire model; Ornstein–Uhlenbeck process; Firing densities; Volterra integral equation; Simulation (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:799-809

DOI: 10.1016/j.amc.2014.01.143

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