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

Author

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

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.

Suggested Citation

  • Buonocore, A. & Caputo, L. & Nobile, A.G. & Pirozzi, E., 2014. "Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 799-809.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:799-809
    DOI: 10.1016/j.amc.2014.01.143
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    References listed on IDEAS

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    1. Schindler, Michael & Talkner, Peter & Hänggi, Peter, 2005. "Escape rates in periodically driven Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(1), pages 40-50.
    2. Aniello Buonocore & Luigia Caputo & Enrica Pirozzi & Luigi M. Ricciardi, 2011. "The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 29-57, March.
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    Cited by:

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    2. Zhongda, Tian & Shujiang, Li & Yanhong, Wang & Yi, Sha, 2017. "A prediction method based on wavelet transform and multiple models fusion for chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 158-172.
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    6. Virginia Giorno & Amelia G. Nobile, 2021. "On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes," Mathematics, MDPI, vol. 9(8), pages 1-25, April.

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