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• W3044802916 abstract "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 $delta rightarrow 0$. All filters require the solution of a Poisson equation defined on $mathbb{R}^{d}$, 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." @default.
• W3044802916 created "2020-07-29" @default.
• W3044802916 creator A5011282941 @default.
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• W3044802916 creator A5087316749 @default.
• W3044802916 date "2020-07-24" @default.
• W3044802916 modified "2023-09-27" @default.
• W3044802916 title "McKean-Vlasov SDEs in nonlinear filtering" @default.
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• W3044802916 hasPublicationYear "2020" @default.
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