"Everything should be made as simple as possible, but not simpler." - Albert Einstein

Seminar Announcement

Convergence of Ensemble Kalman Filter

Jan Mandel, University of Colorado, Denver

Monday, October 5, 2009

4:00 p.m., 223 Weber

ABSTRACT

Based on joint work with Loren Cobb and Jonathan Beezley.

Convergence of the ensemble Kalman filter (EnKF) 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.

In practice, the EnKF is of interest primarily in very high dimension. However, the convergence analysis is formulated using weak convergence in the given fixed state space, and so it does not provide convergence uniformly with respect to the dimension of the state space. This motivates ongoing work on extending the theory to infinitely
dimensional Hilbert space, and the the talk will discuss some recent progress.