The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field McKean-Vlasov type particle interpretation of the Kalman-Bucy diffusions. Besides some recent advances on the stability of nonlinear Langevin type diffusions with drift interactions, the long-time behaviour of models with interacting diffusion matrices and conditional distribution interaction functions has never been discussed in the literature. One of the main contributions of the talk is to initiate the study of this new class of models The talk presents a series of new functional inequalities to quantify the stability of these nonlinear diffusion processes. The second contribution of this talk is to provide uniform propagation of chaos properties as well as Lp-mean error estimates w.r.t. to the time horizon.
Bienvenue à tous!