On the parameter estimation for diffusion models of single neuron's activities. I: Application to spontaneous activities of mesencephalic reticular formation cells in sleep and waking states

DOI10.1007/BF00201423zbMath0827.92009OpenAlexW1548611360MaRDI QIDQ1899175

Shunsuke Sato, Junko Inoue, Luigi M. Ricciardi

Publication date: 9 November 1995

Published in: Biological Cybernetics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00201423

zbMATH Keywords

tablesWiener modelOrnstein-Uhlenbeck neuronal modelfirst- and second-order momentsinfinitesimal standard deviation per unit timeinterspike interval datamean input per unit timemesencephalic reticular formation

Mathematics Subject Classification ID

Markov processes: estimation; hidden Markov models (62M05) Neural biology (92C20) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

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Cites Work

• Unnamed Item
• Unnamed Item
• Stochastic model neuron without resetting of dendritic potential: Application to the olfactory system
• Inference for the diffusion models of neuronal activity
• Statistical inference on spontaneous neuronal discharge patterns
• Diffusion approximation of the neuronal model with synaptic reversal potentials
• Diffusion approximation and first-passage-time problem for a model neuron. III: A birth-and-death process approach
• Optimal estimation for semimartingale neuronal models
• Diffusion approximation for a multi-input model neuron
• A point process analysis of the spontaneous activity of anterior semicircular canal units in the anesthetized pigeon
• Exponential trends of Ornstein–Uhlenbeck first-passage-time densities
• A new integral equation for the evaluation of first-passage-time probability densities
• First-passage-time density and moments of the ornstein-uhlenbeck process
• Introduction to Theoretical Neurobiology
• Analysis of the exponential decay model of the neuron showing frequency threshold effects
• On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries

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