Abstract
For a class of stationary Gaussian processes and for large correlation times, the asymptotic behavior of the upcrossing first passage time probability densities is investigated. Parallel simulations of sample paths of special stationary Gaussian processes for large correlations times provide a statistical validation of the theoretical results.
This work has been performed under partial support by MIUR (PRIN 2003) and by GNCS-INdAM.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: On a non-Markov neuronal model and its approximation. BioSystems 48, 29–35 (1998)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: A computational approach to first-passage-time problem for Gauss-Markov processes. Adv. Appl. Prob. 33, 453–482 (2001)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: On the asymptotic behavior of first passage time densities for stationary Gaussian processes and varying boundaries. Methodology and Computing in Applied Probability 5, 211–233 (2003)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Computational Methods for the Evaluation of Neuron’s Firing Densities. In: Moreno-Díaz Jr., R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 394–403. Springer, Heidelberg (2003)
Giorno, V., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: Non-stationary Gauss-Markov Processes and Neuronal Modeling. In: Trappl, R. (ed.) Cybernetics and Systems 2004 - EMCSR 2004, pp. 211–215. Austrian Society for Cybernetics Studies, Vienna (2004)
Lansky, P., Smith, C.E.: The effect of a random initial value in neural first-passage-time models. Math. Biosci. 93, 191–215 (1989)
Kostyukov, A.I.: Curve-Crossing Problem for Gaussian Stochastic Processes and its Application to Neural Modelling. Biol. Cybernetics 29, 187–191 (1978)
Kostyukov, A.I., Ivanov, Yu, N., Kryzhanovsky, M.V.: Probability of Neuronal Spike Initiation as a Curve-Crossing Problem for Gaussian Stochastic Processes. Biol. Cybernetics 39, 157–163 (1981)
Ogorodnikov, V.A., Prigarin, S.M.: Numerical Modelling od Random Processes and Fields. Algorithms and Applications. VSP, Uthrecht, The Netherlands (1996)
Ricciardi, L.M.: Diffusion Processes and Related Topics in Biology. Springer, New York (1977)
Ricciardi, L.M., Sato, S.: On the evaluation of first–passage–time densities for Gaussian processes. Signal Processing 11, 339–357 (1986)
Ricciardi, L.M., Lánský, P.: Diffusion models of neuron activity. In: Arbib, M.A. (ed.) The Handbook of Brain Theory and Neural Networks, pp. 343–348. MIT Press, Cambridge (2002)
Roberts, J.B.: An approach to the first-passage problem in random vibration. J. Sound Vib. 8(2), 301–328 (1968)
Ross, S.M.: Simulation. Academic Press, San Diego (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giorno, V., Nobile, A.G., Pirozzi, E. (2005). Upcrossing First Passage Times for Correlated Gaussian Processes. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_58
Download citation
DOI: https://doi.org/10.1007/11556985_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29002-5
Online ISBN: 978-3-540-31829-3
eBook Packages: Computer ScienceComputer Science (R0)