Non-asymptotic stability bounds for multivariate ensemble Kalman filters under Wishart fluctuations
michaelchchoi · x · 2026-09-22
Paper 2 of the JJSD Monte Carlo special issue thread: Del Moral, Nasri & Rémillard develop a self-contained stochastic perturbation theory for discrete-generation, multivariate Ensemble Kalman filters. Unlike continuous-time counterparts, discrete EnKF's two-step prediction–update scheme exhibits non-Gaussian fluctuations even in linear settings, taking the form of non-central Wishart-type perturbations in the multivariate case. Under minimal structural assumptions (allowing unstable dynamics), they establish non-asymptotic, time-uniform stability and error estimates for ensemble covariance processes, quantifying the impact of ensemble size, dimension and observation noise, with explicit long-horizon error bounds via stochastic Riccati difference equations driven by matrix-valued Wishart fluctuations.
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