113 citations · 181 across the 8 of their papers we have counts for
8 papers
Regularisation by fractional noise for one-dimensional differential equations with distributional drift
Lukas Anzeletti, Alexandre Richard, Etienne Tanré
We study existence and uniqueness of solutions to the equation , where is a distribution in some Besov space and is a fractional Brownian motion with…
Hopf bifurcation in a Mean-Field model of spiking neurons
Quentin Cormier, Etienne Tanré, Romain Veltz
We study a family of non-linear McKean-Vlasov SDEs driven by a Poisson measure, modelling the mean-field asymptotic of a network of generalized Integrate-and-Fire neurons. We give…
Penalisation techniques for one-dimensional reflected rough differential equations
Alexandre Richard, Etienne Tanré, Soledad Torres
In this paper we solve real-valued rough differential equations (RDEs) reflected on an irregular boundary. The solution is constructed as the limit of a sequence $(Y^n)_{n\in\m…
Long time behavior of a mean-field model of interacting neurons
Quentin Cormier, Etienne Tanré, Romain Veltz
We study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymp…
On a toy network of neurons interacting through their dendrites
Nicolas Fournier, Etienne Tanré, Romain Veltz
Consider a large number of neurons, each being connected to approximately other ones, chosen at random. When a neuron spikes, which occurs randomly at some rate depending o…
An unbiased Monte Carlo estimator for derivatives. Application to CIR
Victor Reutenauer, Etienne Tanré
In this paper, we present extensions of the exact simulation algorithm introduced by Beskos et al. (2006). First, a modification in the order in which the simulation is done accele…
Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size
Pierre Guiraud, Etienne Tanré
We study the synchronization of fully-connected and totally excitatory integrate and fire neural networks in presence of Gaussian white noises. Using a large deviation principle, w…
Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
François Delarue, James Inglis, Sylvain Rubenthaler +1
We here investigate the well-posedness of a networked integrate-and-fire model describing an infinite population of neurons which interact with one another through their common sta…