Łukasz Madry (LPSM)

Titre : Ergodicity and uniform in time propagation of chaos for singular fractional SDEs

Résumé : We consider the system of interacting particle systems interacting through arbitrarily singular vector field, where particles are equipped with independent realisations of highly volatile fractional Brownian motion. I will present work in progress on the proof of the uniform in time convergence of this system towards the McKean-Vlasov equation as the number of particles goes to infinity. Our method builds up on the techniques used in Hairer 05' to prove existence of the invariant measure of the fractional SDE with the same confining potential and recent progress in the theory of the regularisation by noise. This is joint work with Avi Mayorcas (Bath, UK).