97 citations · 144 across the 19 of their papers we have counts for
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Clarification and complement to "Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons"
Mireille Bossy, Olivier Faugeras, Denis Talay
In this note, we clarify the well-posedness of the limit equations to the mean-field -neuron models proposed in Baladron et al. and we prove the associated propagation of chaos…
On the Hamiltonian structure of large deviations in stochastic hybrid systems
Paul Bressloff, Olivier Faugeras
We develop the connection between large deviation theory and more applied approaches to stochastic hybrid systems by highlighting a common underlying Hamiltonian structure. A stoch…
Asymptotic description of stochastic neural networks. II - Characterization of the limit law
Olivier Faugeras, James MacLaurin
We continue the development, started in of the asymptotic description of certain stochastic neural networks. We use the Large Deviation Principle (LDP) and the good rate function H…
Asymptotic description of stochastic neural networks. I - existence of a Large Deviation Principle
Olivier Faugeras, James MacLaurin
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differe…
Large Deviations of a Spatially-Stationary Network of Interacting Neurons
Olivier Faugeras, James MacLaurin
In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting neurons indexed by a lattice . The neurons are subject to noise,…