Repository: Freie Universität Berlin, Math Department

Rough McKean–Vlasov dynamics for robust ensemble Kalman filtering

Coghi, Michele and Nilssen, Torstein and Nüsken, Nikolas and Reich, Sebastian (2023) Rough McKean–Vlasov dynamics for robust ensemble Kalman filtering. The Annals of Applied Probability, 33 (6b). pp. 5693-5752.

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Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean–Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting particle system, which in turn is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework. Finally, we discuss a data-driven method based on subsampling to construct suitable rough path lifts and demonstrate the robustness of our scheme in a number of numerical experiments related to parameter estimation problems in multiscale contexts.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2807
Deposited By: Monika Drueck
Deposited On:14 Mar 2022 15:29
Last Modified:21 Feb 2024 11:24

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