Mean field limit of Ensemble Square Root filters - discrete and continuous time

Theresa Lange; Wilhelm Stannat

doi:10.3934/fods.2021003

Article Contents

2021, Volume 3, Issue 3: 563-588. Doi: 10.3934/fods.2021003

This issue Previous Article Feedback particle filter for collective inference Next Article A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation

Mean field limit of Ensemble Square Root filters - discrete and continuous time

Theresa Lange^1, , and
Wilhelm Stannat^1,2,

1.
Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
2.
Bernstein Center for Computational Neuroscience, Philippstr. 13, 10115 Berlin, Germany

^* Corresponding author: Theresa Lange
^* Corresponding author: Theresa Lange

Received: November 2020

Revised: January 2021

Early access: January 22, 2021

Published online: January 22, 2021

The research of Theresa Lange and Wilhelm Stannat has been partially funded by Deutsche Forschungsgemeinschaft (DFG) - SFB1294/1 - 318763901

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Abstract

Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals, partially observed with linear observations corrupted with independent measurement noise. We analyze the asymptotic behavior of these algorithms in the large ensemble limit both in discrete and continuous time. We identify limiting mean-field processes on the level of the ensemble members, prove corresponding propagation of chaos results and derive associated convergence rates in terms of the ensemble size. In continuous time we also identify the stochastic partial differential equation driving the distribution of the mean-field process and perform a comparison with the Kushner-Stratonovich equation.

Keywords:

Mathematics Subject Classification: 60H35, 93E11, 60F99.

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References

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