Derivation of Ensemble Kalman-Bucy Filters with unbounded nonlinear coefficients

TL;DR

This paper rigorously derives continuous-time limits of ensemble Kalman filters with nonlinear, unbounded coefficients, establishing convergence, well-posedness, and accuracy of these filters in both discrete and continuous forms.

Contribution

It provides the first rigorous derivation and convergence analysis of ensemble Kalman-Bucy filters with nonlinear, unbounded operators, linking discrete and continuous formulations.

Findings

Established convergence rates in discretization step size.

Proved well-posedness of the continuous-time filters.

Demonstrated accuracy of the filters in nonlinear, unbounded settings.

Abstract

We provide a rigorous derivation of the Ensemble Kalman-Bucy Filter as well as the Ensemble Transform Kalman-Bucy Filter in case of nonlinear, unbounded model and observation operators. We identify them as the continuous time limit of the discrete-time Ensemble Kalman Filter and the Ensemble Square Root Filters, respectively, together with concrete convergence rates in terms of the discretization step size. Simultaneously, we establish well-posedness as well as accuracy of both the continuous-time and the discrete-time filtering algorithms.