On two diffusion neuronal models with multiplicative noise: The mean first-passage time properties

DOI10.1063/1.5009574zbMath1390.92028OpenAlexW2795492088WikidataQ92448548 ScholiaQ92448548MaRDI QIDQ4565969

Enrica Pirozzi, Giuseppe D'Onofrio, Petr Lansky

Publication date: 13 June 2018

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2318/1702586

zbMATH Keywords

diffusion processesmultiplicative noisemembrane depolarization

Mathematics Subject Classification ID

Neural biology (92C20) Diffusion processes (60J60) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (11)

Inhibition enhances the coherence in the Jacobi neuronal model ⋮ The Jacobi diffusion process as a neuronal model ⋮ A cumulant approach for the first-passage-time problem of the Feller square-root process ⋮ An adaptive splitting method for the Cox-Ingersoll-Ross process ⋮ Some notes about inference for the lognormal diffusion process with exogenous factors ⋮ Deterministic control of SDEs with stochastic drift and multiplicative noise: a variational approach ⋮ Stochastic transitions between in-phase and anti-phase synchronization in coupled map-based neural oscillators ⋮ An optimal Gauss-Markov approximation for a process with stochastic drift and applications ⋮ Asymptotic results for first-passage times of some exponential processes ⋮ Time-inhomogeneous Feller-type diffusion process with absorbing boundary condition ⋮ Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motion

Uses Software

• hypergeo

Cites Work

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• Successive spike times predicted by a stochastic neuronal model with a variable input signal
• A numerical method for some stochastic differential equations with multiplicative noise
• The effect of mean reversion on investment under uncertainty
• An option pricing formula for the GARCH diffusion model
• 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
• Special issue: Proceedings of the NATO ASI workshop: Stochastic resonance in physics and biology. San Diego, CA, USA, March 30--April 3, 1992
• Stochastic resonance in neuron models
• Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics
• Survival models based on the Ornstein-Uhlenbeck process
• A real options approach to the valuation of a forestry investment.
• 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
• On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity
• Entropy factor for randomness quantification in neuronal data
• The special functions and their approximations. Vol. I, II
• On a set of data for the membrane potential in a neuron
• Two singular diffusion problems
• Estimating the Nitrous Oxide Emission Rate from the Soil Surface by Means of a Diffusion Model
• A Theory of the Term Structure of Interest Rates
• Estimation of the input parameters in the Feller neuronal model
• On a Stochastic Leaky Integrate-and-Fire Neuronal Model
• Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise
• First-passage-time densities for time-non-homogeneous diffusion processes
• THE SPECTRAL DECOMPOSITION OF THE OPTION VALUE
• Spiking Neuron Models
• Derivatives of any order of the confluent hypergeometric function F11(a,b,z) with respect to the parameter a or b

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