On the stability of matrix-valued Riccati diffusions

Bishop, AN; Del Moral, P

On the stability of matrix-valued Riccati diffusions

Bishop, AN

Del Moral, P

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Publication Type:: Journal Article
Citation:: Electronic Journal of Probability, 2019, 24
Issue Date:: 2019-01-01

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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.date.accessioned	2020-03-18T04:26:00Z
dc.date.available	2020-03-18T04:26:00Z
dc.date.issued	2019-01-01	en_US
dc.identifier.citation	Electronic Journal of Probability, 2019, 24	en_US
dc.identifier.uri	http://hdl.handle.net/10453/139387
dc.description.abstract	© 2019, Institute of Mathematical Statistics. All rights reserved. The stability properties of matrix-valued Riccati diffusions are investigated. The matrix-valued Riccati diffusion processes considered in this work are of interest in their own right, as a rather prototypical model of a matrix-valued quadratic stochastic process. Under rather natural observability and controllability conditions, we derive time-uniform moment and fluctuation estimates and exponential contraction inequalities. Our approach combines spectral theory with nonlinear semigroup methods and stochastic matrix calculus. This analysis seem to be the first of its kind for this class of matrix-valued stochastic differential equation. This class of stochastic models arise in signal processing and data assimilation, and more particularly in ensemble Kalman-Bucy filtering theory. In this context, the Riccati diffusion represents the flow of the sample covariance matrices associated with McKean-Vlasov-type interacting Kalman-Bucy filters. The analysis developed here applies to filtering problems with unstable signals.	en_US
dc.relation.ispartof	Electronic Journal of Probability	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject.classification	Statistics & Probability	en_US
dc.title	On the stability of matrix-valued Riccati diffusions	en_US
dc.type	Journal Article
utslib.citation.volume	24	en_US
utslib.for	0104 Statistics	en_US
utslib.for	0105 Mathematical Physics	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.publication-status	Published	en_US
pubs.volume	24	en_US

Abstract:

© 2019, Institute of Mathematical Statistics. All rights reserved. The stability properties of matrix-valued Riccati diffusions are investigated. The matrix-valued Riccati diffusion processes considered in this work are of interest in their own right, as a rather prototypical model of a matrix-valued quadratic stochastic process. Under rather natural observability and controllability conditions, we derive time-uniform moment and fluctuation estimates and exponential contraction inequalities. Our approach combines spectral theory with nonlinear semigroup methods and stochastic matrix calculus. This analysis seem to be the first of its kind for this class of matrix-valued stochastic differential equation. This class of stochastic models arise in signal processing and data assimilation, and more particularly in ensemble Kalman-Bucy filtering theory. In this context, the Riccati diffusion represents the flow of the sample covariance matrices associated with McKean-Vlasov-type interacting Kalman-Bucy filters. The analysis developed here applies to filtering problems with unstable signals.

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http://hdl.handle.net/10453/139387