On the Convergence of the Ensemble Kalman Filter

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, Slutsky's theorem gives weak convergence of ensemble members, and $L^p$ bounds on the ensemble then give $L^p$ convergence.