Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications

DOI10.1007/978-3-642-32157-3_5zbMath1390.92032arXiv1101.5539OpenAlexW2962963470WikidataQ105584924 ScholiaQ105584924MaRDI QIDQ4567932

Maria Teresa Giraudo, Laura Sacerdote

Publication date: 20 June 2018

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5539

zbMATH Keywords

integrate and fire modelsclosed forms expressions

Mathematics Subject Classification ID

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

Related Items (35)

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Cites Work

• Unnamed Item
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• On the classification of experimental data modeled via a stochastic leaky integrate and fire model through boundary values
• Diffusion approximation and first passage time problem for a model neuron. II. Outline of a computation method
• Almost sure comparisons for first passage times of diffusion processes through boundaries
• The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time
• A fast algorithm for the first-passage times of Gauss-Markov processes with Hölder continuous boundaries
• On the transformation of diffusion equations and boundaries into the Kolmogorov equation for the Wiener process
• Inference for the diffusion models of neuronal activity
• On the inverse first-passage-time problem for a Wiener process
• The parameters of the stochastic leaky integrate-and-fire neuronal model
• Boundary-crossing identities for diffusions having the time-inversion property
• A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models
• Special issue on quantitative neuron modeling
• First-passage-time location function: application to determine first-passage-time densities in diffusion processes
• On the asymptotic behavior of the parameter estimators for some diffusion processes: application to neuronal models
• Boundary crossing of Brownian motion. Its relation to the law of the iterated logarithm and to sequential analysis
• 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
• Sequential tests constructed from images
• On the transformation of diffusion processes into the Feller process
• On the transformation of diffusion processes into the Wiener process
• The spatial properties of a model neuron increase its coding range
• A qualitative comparison of some diffusion models for neural activity via stochastic ordering.
• A Monte Carlo method for the simulation of first passage times of diffusion processes
• Limit at zero of the Brownian first-passage density
• Asymptotics of hitting probabilities for general one-dimensional pinned diffusions
• Noise induced synchronization in a neuronal oscillator
• 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
• A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties
• A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input
• An approximate formula for the first-crossing-time density of a Wiener process perturbed by random jumps
• On a set of data for the membrane potential in a neuron
• Les fonctions aléatoires du type de Markoff associees à certaines équations linéaires aux dérivées partielles du type parabolique
• On a discrimination problem for a class of stochastic processes with ordered first-passage times
• Estimation of the input parameters in the Feller neuronal model
• On a Stochastic Leaky Integrate-and-Fire Neuronal Model
• On an integral equation for first-passage-time probability densities
• On certain bounds for first-crossing-time probabilities of a jump-diffusion process
• Parameters of the Diffusion Leaky Integrate-and-Fire Neuronal Model for a Slowly Fluctuating Signal
• Simplicity and Efficiency of Integrate-and-Fire Neuron Models
• Maximum Likelihood Decoding of Neuronal Inputs from an Interspike Interval Distribution
• MEAN VARIANCE AND SKEWNESS OF THE FIRST PASSAGE TIME FOR THE ORNSTEIN-UHLENBECK PROCESS
• Exponential trends of Ornstein–Uhlenbeck first-passage-time densities
• Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution
• The first-passage density of a continuous gaussian process to a general boundary
• Some remarks on the Rayleigh process
• A new integral equation for the evaluation of first-passage-time probability densities
• FIRST PASSAGE TIME PROBLEMS AND SOME RELATED COMPUTATIONAL METHODS
• The first-passage density of the Brownian motion process to a curved boundary
• Introduction to Theoretical Neurobiology
• Evaluation of the first-passage time probability to a square root boundary for the Wiener process
• A symmetry-based constructive approach to probability densities for one-dimensional diffusion processes
• Asymptotic behaviour of ornstein‐uhlenbeck first‐passage‐time density through periodic boundaries
• Boundary crossing probability for Brownian motion and general boundaries
• First-passage-time densities for time-non-homogeneous diffusion processes
• Interspike Interval Correlations, Memory, Adaptation, and Refractoriness in a Leaky Integrate-and-Fire Model with Threshold Fatigue
• An improved technique for the simulation of first passage times for diffusion processes
• On the solution of the Fokker–Planck equation for a Feller process
• Spiking Neuron Models
• On evaluations and asymptotic approximations of first-passage-time probabilities
• Estimation in Discretely Observed Diffusions Killed at a Threshold
• How Sample Paths of Leaky Integrate-and-Fire Models Are Influenced by the Presence of a Firing Threshold
• Parameters of Spike Trains Observed in a Short Time Window
• The minimum of a stationary Markov process superimposed on a U-shaped trend
• Diffusion approximation and first passage time problem for a model neuron
• Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test
• On the numerical solution of Brownian motion processes
• Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process¹
• On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries
• On the First Passage Time Probability Problem
• The Ornstein-Uhlenbeck neuronal model with signal-dependent noise

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