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Perturbations and projections of Kalman–Bucy semigroups

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  • Bishop, Adrian N.
  • Del Moral, Pierre
  • Pathiraja, Sahani D.

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.

Suggested Citation

  • Bishop, Adrian N. & Del Moral, Pierre & Pathiraja, Sahani D., 2018. "Perturbations and projections of Kalman–Bucy semigroups," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2857-2904.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:9:p:2857-2904
    DOI: 10.1016/j.spa.2017.10.006
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Del Moral, P. & Singh, S.S., 2022. "Backward Itô–Ventzell and stochastic interpolation formulae," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 197-250.

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