Academic
Publications
The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model

The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model,10.1007/s11009-009-9132-8,

The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model   (Citations: 2)
BibTex | RIS | RefWorks Download
Motivated by some unsolved problems of biological interest, such as the description of firing probability densities for Leaky Integrate-and-Fire neuronal models, we consider the first-passage-time problem for Gauss-diffusion processes along the line of Mehr and McFadden (J R Stat Soc B 27:505–522, 1965). This is essentially based on a space-time transformation, originally due to Doob (Ann Math Stat 20:393–403, 1949), by which any Gauss-Markov process can expressed in terms of the standard Wiener process. Starting with an analysis that pinpoints certain properties of mean and autocovariance of a Gauss-Markov process, we are led to the formulation of some numerical and time-asymptotically analytical methods for evaluating first-passage-time probability density functions for Gauss-diffusion processes. Implementations for neuronal models under various parameter choices of biological significance confirm the expected excellent accuracy of our methods.
Cumulative Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
    • ...Motivated by biological problems, and especially by those related to LIF neuronal models, the FPT problem for Gauss-diffusion processes was recently taken up afresh by us [2] both via space-time transformations to the Ornstein-Uhlenbeck (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 Buonocoreet al. On a Generalized Leaky Integrate-and-Fire Model for Single Neuron Acti...

  • Sort by: