A discrete time neural network model with spiking neurons. II: Dynamics with noise. (English) Zbl 1230.92012
[For part I see ibid. 56, No. 3, 311–345 (2008; Zbl 1145.37342).]
Summary: We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate-and-fire neurons, where time is discrete and where neurons are submitted to noise, without restrictions on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike train statistics.
Summary: We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate-and-fire neurons, where time is discrete and where neurons are submitted to noise, without restrictions on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike train statistics.
Citations:
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