Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications (Q4567932)

scientific article; zbMATH DE number 6891912

Language	Label	Description	Also known as
English	Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications	scientific article; zbMATH DE number 6891912

Statements

instance of

scholarly article

0 references

title

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

0 references

0 references

0 references

Lecture Notes in Mathematics

0 references

publication date

20 June 2018

0 references

full work available at URL

https://arxiv.org/abs/1101.5539

0 references

zbMATH Keywords

integrate and fire models

0 references

closed forms expressions

0 references

MaRDI profile type

MaRDI publication profile

0 references

cites work

Q3331506

0 references

Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process<sup>1</sup>

0 references

Boundary-crossing identities for diffusions having the time-inversion property

0 references

On the numerical solution of Brownian motion processes

0 references

Asymptotics of hitting probabilities for general one-dimensional pinned diffusions

0 references

Estimation in Discretely Observed Diffusions Killed at a Threshold

0 references

Q4396365

0 references

A new integral equation for the evaluation of first-passage-time probability densities

0 references

On a Stochastic Leaky Integrate-and-Fire Neuronal Model

0 references

A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input

0 references

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

0 references

Diffusion approximation and first passage time problem for a model neuron

0 references

On the transformation of diffusion processes into the Feller process

0 references

MEAN VARIANCE AND SKEWNESS OF THE FIRST PASSAGE TIME FOR THE ORNSTEIN-UHLENBECK PROCESS

0 references

Interspike Interval Correlations, Memory, Adaptation, and Refractoriness in a Leaky Integrate-and-Fire Model with Threshold Fatigue

0 references

Q4131341

0 references

The minimum of a stationary Markov process superimposed on a U-shaped trend

0 references

Sequential tests constructed from images

0 references

On a discrimination problem for a class of stochastic processes with ordered first-passage times

0 references

On certain bounds for first-crossing-time probabilities of a jump-diffusion process

0 references

Estimation of the input parameters in the Feller neuronal model

0 references

Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test

0 references

The first-passage density of a continuous gaussian process to a general boundary

0 references

The first-passage density of the Brownian motion process to a curved boundary

0 references

FIRST PASSAGE TIME PROBLEMS AND SOME RELATED COMPUTATIONAL METHODS

0 references

Les fonctions aléatoires du type de Markoff associees à certaines équations linéaires aux dérivées partielles du type parabolique

0 references

Spiking Neuron Models

0 references

Some remarks on the Rayleigh process

0 references

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

0 references

A symmetry-based constructive approach to probability densities for one-dimensional diffusion processes

0 references

On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries

0 references

On the asymptotic behavior of the parameter estimators for some diffusion processes: application to neuronal models

0 references

An improved technique for the simulation of first passage times for diffusion processes

0 references

A Monte Carlo method for the simulation of first passage times of diffusion processes

0 references

An approximate formula for the first-crossing-time density of a Wiener process perturbed by random jumps

0 references

How Sample Paths of Leaky Integrate-and-Fire Models Are Influenced by the Presence of a Firing Threshold

0 references

First-passage-time densities for time-non-homogeneous diffusion processes

0 references

On a set of data for the membrane potential in a neuron

0 references

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

0 references

Q5134772

0 references

Special issue on quantitative neuron modeling

0 references

Q3040970

0 references

Q3923307

0 references

Q4004325

0 references

Inference for the diffusion models of neuronal activity

0 references

Diffusion approximation of the neuronal model with synaptic reversal potentials

0 references

The spatial properties of a model neuron increase its coding range

0 references

On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity

0 references

The Ornstein-Uhlenbeck neuronal model with signal-dependent noise

0 references

The parameters of the stochastic leaky integrate-and-fire neuronal model

0 references

A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models

0 references

Boundary crossing of Brownian motion. Its relation to the law of the iterated logarithm and to sequential analysis

0 references

Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution

0 references

Exponential trends of Ornstein–Uhlenbeck first-passage-time densities

0 references

Noise induced synchronization in a neuronal oscillator

0 references

Parameters of Spike Trains Observed in a Short Time Window

0 references

Limit at zero of the Brownian first-passage density

0 references

Parameters of the Diffusion Leaky Integrate-and-Fire Neuronal Model for a Slowly Fluctuating Signal

0 references

Simplicity and Efficiency of Integrate-and-Fire Neuron Models

0 references

On the transformation of diffusion processes into the Wiener process

0 references

Q4127741

0 references

The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time

0 references

Diffusion approximation and first passage time problem for a model neuron. II. Outline of a computation method

0 references

On an integral equation for first-passage-time probability densities

0 references

0 references

0 references

0 references

0 references

First-passage-time location function: application to determine first-passage-time densities in diffusion processes

0 references

Asymptotic behaviour of ornstein‐uhlenbeck first‐passage‐time density through periodic boundaries

0 references

On the solution of the Fokker–Planck equation for a Feller process

0 references

On the transformation of diffusion equations and boundaries into the Kolmogorov equation for the Wiener process

0 references

Q4662079

0 references

A qualitative comparison of some diffusion models for neural activity via stochastic ordering.

0 references

Almost sure comparisons for first passage times of diffusion processes through boundaries

0 references

On evaluations and asymptotic approximations of first-passage-time probabilities

0 references

Q4662078

0 references

On the classification of experimental data modeled via a stochastic leaky integrate and fire model through boundary values

0 references

Evaluation of the first-passage time probability to a square root boundary for the Wiener process

0 references

Q3755269

0 references

On the First Passage Time Probability Problem

0 references

A fast algorithm for the first-passage times of Gauss-Markov processes with Hölder continuous boundaries

0 references

Introduction to Theoretical Neurobiology

0 references

Boundary crossing probability for Brownian motion and general boundaries

0 references

Maximum Likelihood Decoding of Neuronal Inputs from an Interspike Interval Distribution

0 references

On the inverse first-passage-time problem for a Wiener process

0 references

Identifiers

zbMATH Open document ID

1390.92032

0 references

DOI

10.1007/978-3-642-32157-3_5

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:4567932