### On the continuous time limit of ensemble square root filters

Lange T, Stannat W (2021)
Communications in Mathematical Sciences 19(7): 1855-1880.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Lange, TheresaUniBi; Stannat, Wilhelm
Einrichtung
Abstract / Bemerkung
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-Bucy filtering equations introduced in [J. de Wiljes, S. Reich, and W. Stannat, SIAM J. Appl. Dyn. Syst., 17(2):1152-1181, 2018]. The latter result can be generalized to nonlinear Lipschitz-continuous model operators. A striking implication of our results is the fact that the limiting equations for the ensemble members are universal for a large class of ensemble square root filters. This yields a mathematically rigorous justification for the analysis of these algorithms with the help of the ensemble Kalman-Bucy filter.
Stichworte
Continuous time limit; Ensemble square root filter; Deterministic model; perturbations
Erscheinungsjahr
2021
Zeitschriftentitel
Communications in Mathematical Sciences
Band
19
Ausgabe
7
Seite(n)
1855-1880
ISSN
1539-6746
Page URI
https://pub.uni-bielefeld.de/record/2957738

### Zitieren

Lange T, Stannat W. On the continuous time limit of ensemble square root filters. Communications in Mathematical Sciences. 2021;19(7):1855-1880.
Lange, T., & Stannat, W. (2021). On the continuous time limit of ensemble square root filters. Communications in Mathematical Sciences, 19(7), 1855-1880. https://doi.org/10.4310/CMS.2021.v19.n7.a5
Lange, T., and Stannat, W. (2021). On the continuous time limit of ensemble square root filters. Communications in Mathematical Sciences 19, 1855-1880.
Lange, T., & Stannat, W., 2021. On the continuous time limit of ensemble square root filters. Communications in Mathematical Sciences, 19(7), p 1855-1880.
T. Lange and W. Stannat, “On the continuous time limit of ensemble square root filters”, Communications in Mathematical Sciences, vol. 19, 2021, pp. 1855-1880.
Lange, T., Stannat, W.: On the continuous time limit of ensemble square root filters. Communications in Mathematical Sciences. 19, 1855-1880 (2021).
Lange, Theresa, and Stannat, Wilhelm. “On the continuous time limit of ensemble square root filters”. Communications in Mathematical Sciences 19.7 (2021): 1855-1880.

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