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Perturbations and projections of Kalman–Bucy semigroups

Abstract : We analyse various perturbations and projections of Kalman–Bucy semigroups and Riccati equations. For example, covariance inflation-type perturbations and localisation methods (projections) are common in the ensemble Kalman filtering literature. In the limit of these ensemble methods, the regularised sample covariance tends toward a solution of a perturbed/projected Riccati equation. With this motivation, results are given characterising the error between the nominal and regularised Riccati flows and Kalman–Bucy filtering distributions. New projection-type models are also discussed; e.g. Bose–Mesner projections. These regularisation models are also of interest on their own, and in, e.g., differential games, control of stochastic/jump processes, and robust control.
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Submitted on : Wednesday, December 20, 2017 - 3:20:32 PM
Last modification on : Friday, July 8, 2022 - 10:06:15 AM

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Adrian N Bishop, Pierre del Moral, Sahani D. Pathiraja. Perturbations and projections of Kalman–Bucy semigroups. Stochastic Processes and their Applications, Elsevier, 2017, pp.1-48. ⟨10.1016/⟩. ⟨hal-01669084⟩



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