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math.PR2019
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…
math.PR2018
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…
math.PR2018
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…