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Keywords
(11)
Analytical Method
Diffusion Process
First Passage Time
Markov Process
Numerical Approximation
Probability Density
Probability Density Function
Wiener Process
Gaussian Process
Leaky Integrate and Fire
Space Time
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The First Passage Time Problem for GaussDiffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model
The First Passage Time Problem for GaussDiffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model,10.1007/s1100900991328,
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The First Passage Time Problem for GaussDiffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model
(
Citations: 2
)
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Aniello Buonocore
,
Luigia Caputo
,
Enrica Pirozzi
,
Luigi M. Ricciardi
Motivated by some unsolved problems of biological interest, such as the description of firing probability densities for Leaky IntegrateandFire neuronal models, we consider the firstpassagetime problem for Gaussdiffusion processes along the line of Mehr and McFadden (J R Stat Soc B 27:505–522, 1965). This is essentially based on a spacetime transformation, originally due to Doob (Ann Math Stat 20:393–403, 1949), by which any GaussMarkov process can expressed in terms of the standard Wiener process. Starting with an analysis that pinpoints certain properties of mean and autocovariance of a GaussMarkov process, we are led to the formulation of some numerical and timeasymptotically analytical methods for evaluating firstpassagetime
probability density
functions for Gaussdiffusion processes. Implementations for neuronal models under various parameter choices of biological significance confirm the expected excellent accuracy of our methods.
Journal:
Methodology and Computing in Applied Probability  METHODOL COMPUT APPL PROBAB
, vol. 13, no. 1, pp. 2957, 2011
DOI:
10.1007/s1100900991328
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Citation Context
(2)
...Functions m
_{V}
(t), u
_{V}
(t) and v
_{V}
(t) can be seen (Buonocore, Caputo, Pirozzi, & Ricciardi,
2009
) to satisfy system
Aniello Buonocore
,
et al.
On a Stochastic Leaky IntegrateandFire Neuronal Model
...Motivated by biological problems, and especially by those related to LIF neuronal models, the FPT problem for Gaussdiffusion processes was recently taken up afresh by us [
2
] both via spacetime transformations to the OrnsteinUhlenbeck (OU) process and in algorithmic terms...
...In conclusion, the time course of the membrane potential is represented by the Gaussian process specified by mean mV(t ): =E [V (t)] and autocovariance cV(τ, t ): =E {[V (τ ) − mV(τ )] [V (t) − mV(t)]} that (see, for instance, [6]) is the product of two functions: uV(τ )a ndvV(t), for all pairs (τ, t) such that τ ≤ t. In addition, functions m(t), u(t )a ndv(t) satisfy system (41) in [
2
]...
...The comparisons can then be performed by implementing the computational methods described for instance in [
2
], or by relying on simulation procedures based on repeatedly solved the respective stochastic differential equations by suitably discretizing meshes...
Aniello Buonocore
,
et al.
On a Generalized Leaky IntegrateandFire Model for Single Neuron Acti...
References
(19)
On the First Passage Time Probability Problem
(
Citations: 86
)
Arnold Siegert
Journal:
Physical Review  PHYS REV X
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Ramp crossings for Slepian's process (Corresp.)
(
Citations: 3
)
J. Abrahams
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 30, no. 3, pp. 574575, 1984
On the transformation of diffusion processes into the Wiener process
(
Citations: 14
)
L RICCIARDI
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 54, no. 1, pp. 185199, 1976
Escape rates in periodically driven Markov processes
(
Citations: 4
)
Michael Schindler
,
Peter Talkner
,
Peter Hanggi
Published in 2009.
Diffusion approximation to a queueing system with timedependent arrival and service rates
(
Citations: 11
)
Antonio Di Crescenzo
,
Amelia G. Nobile
Journal:
Queueing Systems  Theory and Applications  QUESTA
, vol. 19, no. 12, pp. 4162, 1995
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Citations
(2)
On a Stochastic Leaky IntegrateandFire Neuronal Model
(
Citations: 2
)
Aniello Buonocore
,
Ludovico Caputo
,
Enrica Pirozzi
,
Luigi M. Ricciardi
Journal:
Neural Computation  NECO
, vol. 22, no. 10, pp. 25582585, 2010
On a Generalized Leaky IntegrateandFire Model for Single Neuron Activity
Aniello Buonocore
,
Luigia Caputo
,
Enrica Pirozzi
,
Luigi M. Ricciardi
Conference:
Conference On Computer Aided Systems Theory  EUROCAST
, pp. 152158, 2009