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| I will talk about filtering a continuous-time stochastic process which is observed at discrete observation times. A mean-field ensemble Kalman filter (EnKF) is introduced, and a deterministic discretization of its density is proven to asymptotically recover the filtering distribution more accurately than the traditional finite-ensemble Monte Carlo version, for sufficiently low dimensional state-space. This improvement is lost when the underlying distribution deviates from Gaussian, due to the intrinsic assumptions in the EnKF methodology. However, the analogous deterministic discretization of the true filtering density is proven to be both consistent and asymptotically more accurate than the analogous particle methods. The prospect of extension to higher-dimensional state-spaces will be discussed. |
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