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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the continuous time limit of the ensemble Kalman filter
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by Theresa Lange and Wilhelm Stannat HTML | PDF
Math. Comp. 90 (2021), 233-265 Request permission


We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by Burgers, van Leeuwen, and Evensen [Monthly Weather Review 126 (1998), pp. 1719–1724] as well as a recent variant of de Wiljes, Reich, and Stannat [SIAM J. Appl. Dyn. Syst. 17 (2018), no. 2, pp. 1152–1181] to the respective discretizations and show that in the limit of decreasing stepsize the filter equations converge to an ensemble of interacting (stochastic) differential equations in the ensemble-mean-square sense. Our analysis also allows for the derivation of convergence rates with respect to the stepsize.

An application of our analysis is the rigorous derivation of continuous-time ensemble filtering algorithms consistent with discrete-time approximation schemes. Conversely, the continuous time limit allows for a better qualitative and quantitative analysis of the discrete-time counterparts using the rich theory of dynamical systems in continuous time.

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Additional Information
  • Theresa Lange
  • Affiliation: Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
  • Email:
  • Wilhelm Stannat
  • Affiliation: Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany; and Bernstein Center for Computational Neuroscience, Philippstr. 13, D-10115 Berlin, Germany
  • MR Author ID: 357144
  • Email:
  • Received by editor(s): December 14, 2018
  • Received by editor(s) in revised form: January 13, 2020
  • Published electronically: October 6, 2020
  • Additional Notes: The research of both authors was partially funded by Deutsche Forschungsgemeinschaft (DFG) - SFB1294/1 - 318763901.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 233-265
  • MSC (2010): Primary 60H35, 93E11, 60F99
  • DOI:
  • MathSciNet review: 4166460