Perturbations and projections of Kalman–Bucy semigroups

Bishop, AN; Del Moral, P; Pathiraja, SD

Perturbations and projections of Kalman–Bucy semigroups

Bishop, AN

Del Moral, P Pathiraja, SD

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Publication Type:: Journal Article
Citation:: Stochastic Processes and their Applications, 2018, 128 (9), pp. 2857 - 2904
Issue Date:: 2018-09-01

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Field	Value	Language
dc.contributor.author	Bishop, AN https://orcid.org/0000-0001-8581-8562	en_US
dc.contributor.author	Del Moral, P	en_US
dc.contributor.author	Pathiraja, SD	en_US
dc.date.available	2020-09-01T19:01:51Z
dc.date.issued	2018-09-01	en_US
dc.identifier.citation	Stochastic Processes and their Applications, 2018, 128 (9), pp. 2857 - 2904	en_US
dc.identifier.issn	0304-4149	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132478
dc.description.abstract	© 2017 Elsevier B.V. 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.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DE120102873
dc.relation.ispartof	Stochastic Processes and their Applications	en_US
dc.relation.isbasedon	10.1016/j.spa.2017.10.006	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject.classification	Statistics & Probability	en_US
dc.title	Perturbations and projections of Kalman–Bucy semigroups	en_US
dc.type	Journal Article
utslib.citation.volume	9	en_US
utslib.citation.volume	128	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1502 Banking, Finance and Investment	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
utslib.copyright.status	open_access	*
pubs.issue	9	en_US
pubs.publication-status	Published	en_US
pubs.volume	128	en_US

Abstract:

© 2017 Elsevier B.V. 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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http://hdl.handle.net/10453/132478