On the Convergence of the Ensemble Kalman Filter

Details On the Convergence of the Ensemble Kalman Filter On the Convergence of the Ensemble Kalman Filter

2009-01-20

arxiv.org/abs/0901.2951v2

Applications of Mathematics 56, 533-541, 2011

Mathematics

Statistics Theory

Revised, 8 pages

Scientific paper

10.1007/s10492-011-0031-2

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, the continuous mapping theorem gives convergence in probability of the ensemble members, and $L^p$ bounds on the ensemble then give $L^p$ convergence.

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