On Time Non-homogeneous Feller-Type Diffusion Process in Neuronal Modeling

  • Amelia G. NobileEmail author
  • Enrica Pirozzi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9520)


Time non-homogeneous Feller-type and Ornstein-Uhlenbeck diffusion processes are considered for modeling the neuronal activity in the presence of time-varying input signals. In particular, the first passage time (FPT) problem is analyzed for both processes and the averages of FPT through a constant boundary are compared for a constant input signal and for different choices of involved parameters.


  1. 1.
    Buonocore, A., Caputo, L., Pirozzi, E., Ricciardi, L.M.: On a stochastic leaky integrate-and-fire neuronal model. Neural Comput. 22(10), 2558–2585 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Buonocore, A., Caputo, L., Nobile, A.G., Pirozzi, E.: Gauss-Markov processes in the presence of a reflecting boundary and applications in neuronal models. Appl. Math. Comput. 232, 799–809 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Burkitt, A.N.: A review of the integrate-and-fire neuron model. II. Inhomogeneous synaptic input and network properties. Biol. Cybern. 95(2), 97–112 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ditlevsen, S., Lánský, P.: Estimation of the input parameters in the Feller neuronal model. Phys. Rev. E 73(061910), 1–9 (2006)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Giorno, V., Nobile, A.G., Ricciardi, L.M., Sato, S.: On the evaluation of first-passage-time probability densities via non-singular integral equation. Adv. Appl. Prob. 21, 20–36 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Giorno, V., Spina, S.: On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model. Math. Biosci. Eng. 11(2), 285–302 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Giraudo, M.T., Sacerdote, L.: Effect of periodic stimulus on a neuronal diffusion model with signal-dependent noise. BioSystems 79, 73–81 (2005)CrossRefGoogle Scholar
  8. 8.
    Inoue, J., Doi, S.: Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for leaky neuron model. BioSystems 87, 49–57 (2007)CrossRefGoogle Scholar
  9. 9.
    Kobayashi, R., Shinomoto, S., Lánský, P.: Estimation of time-dependent input from neuronal membrane potential. Neural Comput. 23, 3070–3093 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Lánský, P., Ditlevsen, S.: A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models. Biol. Cybern. 99, 253–262 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G.: An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. Math. Japonica 50(2), 247–322 (1999)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dipartimento di Studi e Ricerche Aziendali (Management and Information Technology)Università di SalernoFiscianoItaly
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità di Napoli Federico IINapoliItaly

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