English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper is concerned with the mathematical analysis of continuous timeEnsemble Kalman Filters (EnKBFs) and their mean field limit in an infinitedimensional setting. The signal is determined by a nonlinear Stochastic PartialDifferential Equation (SPDE), which is posed in the standard variationalsetting. Assuming global one-sided Lipschitz conditions and finite dimensionalobservations we first prove the well posedness of both the EnKBF and itscorresponding mean field version. We then investigate the quantitativeconvergence of the EnKBF towards its mean field limit, recovering the ratessuggested by the law of large numbers for bounded observation functions. Themain tool hereby are exponential moment estimates for the empirical covarianceof the EnKBF, which may be of independent interest. In the appendix of thepaper we investigate the connection of the mean field EnKBF and the StochasticFiltering Problem. In particular we derive the Feedback Particle Filter forinfinite dimensional signals and show that the mean field EnKBF can viewed asits constant gain approximation.

On the mean field theory of Ensemble Kalman filters for SPDEs