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The statistics of spikes trains: a stochastic calculus approach

Jonathan Touboul 1, * Olivier Faugeras 1
* Corresponding author
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : We discuss the statistics of spikes trains for different types of integrate-and-fire neurons and different types of synaptic noise models. In cotnrast with the usual approaches in neuroscience, mainly based on statistical physics methods such as the Fokker-Planck equation or the mean-field theory, we chose the point of the view of the stochastic calculus theory to characterize neurons in noisy environments. We present four stochastic calculus techniques that can be used to find the probability distributions attached to the spikes trains. We illustrate the power of these techniques for four types of widely used neuron models. Despite the fact that these techniques are mathematically intricate we believe that they can be useful for answering questions in neuroscience that naturally arise from the variability of neuronal activity. For each technique we indicate its range of application and its limitations
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Contributor : Jonathan Touboul <>
Submitted on : Thursday, June 21, 2007 - 5:38:05 PM
Last modification on : Wednesday, October 14, 2020 - 4:11:45 AM
Long-term archiving on: : Thursday, September 23, 2010 - 4:28:24 PM


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  • HAL Id : inria-00156557, version 3



Jonathan Touboul, Olivier Faugeras. The statistics of spikes trains: a stochastic calculus approach. [Research Report] RR-6224, INRIA. 2007, pp.46. ⟨inria-00156557v3⟩



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