Continuous Time Limit of the Stochastic Ensemble Kalman Inversion: Strong Convergence Analysis

The ensemble Kalman inversion (EKI) method is a for the estimation of unknown parameters in context (Bayesian) inverse problems. approximates underlying measure by an particles and iteratively applies update to evolve (the approximation the) prior into posterior measure. For convergence analysis EKI it common practice derive continuous version, replacing iteration with stochastic differential equation. In this paper we validate approach showing that converges paths time equation considering both nonlinear linear setting, prove probability former moments latter. methods employed do not rely on specific structure can also be applied more general numerical schemes equations.