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Long-time Wasserstein contraction for diffusion processes without global dissipativity
Pierre Monmarché
The fact that a Markov diffusion semi-group on contracts the Wasserstein distance, which has been extensively used to establish uniform-in-time stability estima…
A note on a Vlasov-Fokker-Planck equation with non-symmetric interaction
Pierre Monmarché
In the recent [3], Cesbron and Herda study a Vlasov-Fokker-Planck (VFP) equation with non-symmetric interaction, introduced in physics to model the distribution of electrons in a s…
Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo in the nonconvex stochastic gradient case
Martin Chak, Pierre Monmarché
Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with stochastic gradients under possibly nonconvex conditions. The…
Wasserstein contraction for the stochastic Morris-Lecar neuron model
Maxime Herda, Pierre Monmarché, Benoît Perthame
Neuron models have attracted a lot of attention recently, both in mathematics and neuroscience. We are interested in studying long-time and large-population emerging properties in…