Abstract:We develop a general probabilistic framework for analyzing propagation of chaos in transport ensemble filters (TEFs), a broad class of interacting particle systems that are used to approximate the sequence of state distributions in hidden Markov models given a history of observations. This class of transport-based filtering algorithms includes the widely used ensemble Kalman filter (EnKF), based on affine updates at each filtering step, as well as the ensemble stochastic map filter (EnSMF), which employs nonlinear updates. For this class, we identify the limiting mean-field dynamics. We then establish non-asymptotic, high-probability, pathwise Wasserstein convergence of the interacting particle system to an i.i.d. ensemble drawn from this mean-field limit at the Monte Carlo rate. Convergence to the mean-field law itself follows with the usual dimension-dependent empirical Wasserstein rate. The proof combines a synchronous coupling construction with stability of moments and tails under conditioning, together with quantitative estimates for the propagation of the underlying dynamics through the interacting particle system. Applying our theory to both the EnKF and the EnSMF yields the first non-asymptotic, high-probability convergence guarantees for TEFs.
From: Frederic J. N. Jorgensen [view email]
[v1]
Wed, 24 Jun 2026 03:24:43 UTC (78 KB)
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