Diffusion approximation and first-passage-time problem for a model neuron. III: A birth-and-death process approach

DOI10.1007/BF00361346zbMath0641.92008WikidataQ51657444 ScholiaQ51657444MaRDI QIDQ1101034

B. George

Publication date: 1988

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

zbMATH Keywords

meanvarianceclosed form expressionscoefficient of variationone-dimensional diffusionlinear driftreturn processasymptotic momentscontinuous limit of a birth-and-death processinfinitesimal variancemoments of the firing timeneuron's membrane potentialneuronal diffusion modelneuronal firing time problemnew computation methodreversal hyperpolarization potentialsingle neuron's activitysteady state p.d.f.

Mathematics Subject Classification ID

Diffusion processes (60J60) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Physiological, cellular and medical topics (92Cxx)

Related Items (20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Diffusion approximation and first passage time problem for a model neuron. II. Outline of a computation method
• The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time
• Diffusion approximation of the neuronal model with synaptic reversal potentials
• Two singular diffusion problems
• On the probability densities of an Ornstein–Uhlenbeck process with a reflecting boundary
• A note on the evaluation of first-passage-time probability densities
• On an integral equation for first-passage-time probability densities
• A note on first-passage time and some related problems
• Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution
• Some remarks on the Rayleigh process
• On some diffusion approximations to queueing systems
• A new integral equation for the evaluation of first-passage-time probability densities
• Diffusion approximation and first passage time problem for a model neuron
• On the First Passage Time Probability Problem

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