Ensemble Kalman Sampler: Mean-field Limit and Convergence Analysis

The ensemble Kalman sampler (EKS) is a method introduced in [Garbuno-Inigo et al., SIAM J. Appl. Dyn. Syst., 19 (2020), pp. 412--441] to find approximately independent and identically distributed samples from target distribution. As of today, why the algorithm works how it converges mostly unknown. continuous version set coupled stochastic differential equations (SDEs). In this paper, we prove well posedness SDE system justify its mean-field limit Fokker--Planck equation, whose long time equilibrium We further demonstrate that convergence rate near optimal ($J^{-1/2}$ with $J$ being number particles). These results, combined in-time equation [J. A. Carrillo U. Vaes, preprint, arXiv:1910.07555, 2019] validity EKS, provide as sampling method.