# On the continuous time limit of ensemble square root filters

@article{Lange2021OnTC, title={On the continuous time limit of ensemble square root filters}, author={Theresa Lange and Wilhelm Stannat}, journal={Communications in Mathematical Sciences}, year={2021} }

We provide a continuous time limit analysis for the class of Ensemble Square Root Filter algorithms with deterministic model perturbations. In the particular linear case, we specify general conditions on the model perturbations implying convergence of the empirical mean and covariance matrix towards their respective counterparts of the Kalman-Bucy Filter. As a second main result we identify additional assumptions for the convergence of the whole ensemble towards solutions of the Ensemble Kalman…

## 10 Citations

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This article investigates EKI convergence in general nonlinear settings and proves that EKI can hit critical points with finite steps in non-convex settings and converges to the global minimizer polynomially fast if the loss function is strongly convex.

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This article proposes and investigates a localized Ensemble Kalman Bucy Filter (l-EnKBF) for nonlinear models with short-range interactions and derives dimension-independent and component-wise error bounds and shows the long time path-wiseerror only has logarithmic dependence on the time range.

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