Under smooth data and Hamiltonian regularity, the value-function error between controlled nonlinear filtering and its N-particle approximation is O(N^{-1/6}) in d=1, O(N^{-1/6}(log N)^{1/3}) in d=2, and O(N^{-1/(3d)}) for d>2.
Randomized filtering and Bellman equa- tion in Wasserstein space for partial observation control problem.Stochastic Processes and their Applications, 129(2):674–711, 2019
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Quantitative Particle Approximation for Controlled Nonlinear Filtering
Under smooth data and Hamiltonian regularity, the value-function error between controlled nonlinear filtering and its N-particle approximation is O(N^{-1/6}) in d=1, O(N^{-1/6}(log N)^{1/3}) in d=2, and O(N^{-1/(3d)}) for d>2.