# McKean-Vlasov SDEs in nonlinear filtering

arXiv: https://arxiv.org/abs/2007.12658 · HTML: https://mlsanity.com/paper/2007.12658/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2020.

## Built on by (most cited first, 7 of 7)

- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [Connections between sequential Bayesian inference and evolutionary dynamics](https://mlsanity.com/paper/2411.16366/) (2024)
- [Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation](https://mlsanity.com/paper/2106.07908/) (2021)
- [An operator splitting analysis of Wasserstein--Fisher--Rao gradient flows](https://mlsanity.com/paper/2511.18060/) (2025)
- [Pathwise Learning of Stochastic Dynamical Systems with Partial Observations](https://mlsanity.com/paper/2601.21860/) (2026)
- [Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows](https://mlsanity.com/paper/2609.18118/) (2026)

## Abstract (arXiv)

Various particle filters have been proposed over the last couple of decades with the common feature that the update step is governed by a type of control law. This feature makes them an attractive alternative to traditional sequential Monte Carlo which scales poorly with the state dimension due to weight degeneracy. This article proposes a unifying framework that allows to systematically derive the McKean-Vlasov representations of these filters for the discrete time and continuous time observation case, taking inspiration from the smooth approximation of the data considered in Crisan & Xiong (2010) and Clark & Crisan (2005). We consider three filters that have been proposed in the literature and use this framework to derive Ito representations of their limiting forms as the approximation parameter δ rightarrow 0. All filters require the solution of a Poisson equation defined on ℝd, for which existence and uniqueness of solutions can be a non-trivial issue. We additionally establish conditions on the signal-observation system that ensures well-posedness of the weighted Poisson equation arising in one of the filters.