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- Publisher Website: 10.1016/j.jde.2014.01.024
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Article: The contraction rate in Thompson's part metric of order-preserving flows on a cone - Application to generalized Riccati equations
Title | The contraction rate in Thompson's part metric of order-preserving flows on a cone - Application to generalized Riccati equations |
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Authors | |
Keywords | Finsler metric Contraction rate Perron-Frobenius theory Riccati equation Stochastic control Thompson's part metric |
Issue Date | 2014 |
Citation | Journal of Differential Equations, 2014, v. 256, n. 8, p. 2902-2948 How to Cite? |
Abstract | We give a formula for the Lipschitz constant in Thompson's part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This shows that in the special case of order-preserving flows, a general characterization of the contraction rate in Thompson's part metric, given by Nussbaum, leads to an explicit formula. As an application, we show that the flow of the generalized Riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its Lipschitz constant by a matrix inequality. We also show that the same flow is no longer a contraction in other invariant Finsler metrics on this cone, including the standard invariant Riemannian metric. This is motivated by a series of contraction properties concerning the standard Riccati equation, established by Bougerol, Liverani, Wojtkowski, Lawson, Lee and Lim: we show that some of these properties do, and that some other do not, carry over to the generalized Riccati equation. © 2014 Elsevier Inc. |
Persistent Identifier | http://hdl.handle.net/10722/219740 |
ISSN | 2023 Impact Factor: 2.4 2023 SCImago Journal Rankings: 2.046 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Gaubert, Stéphane | - |
dc.contributor.author | Qu, Zheng | - |
dc.date.accessioned | 2015-09-23T02:57:51Z | - |
dc.date.available | 2015-09-23T02:57:51Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Journal of Differential Equations, 2014, v. 256, n. 8, p. 2902-2948 | - |
dc.identifier.issn | 0022-0396 | - |
dc.identifier.uri | http://hdl.handle.net/10722/219740 | - |
dc.description.abstract | We give a formula for the Lipschitz constant in Thompson's part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This shows that in the special case of order-preserving flows, a general characterization of the contraction rate in Thompson's part metric, given by Nussbaum, leads to an explicit formula. As an application, we show that the flow of the generalized Riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its Lipschitz constant by a matrix inequality. We also show that the same flow is no longer a contraction in other invariant Finsler metrics on this cone, including the standard invariant Riemannian metric. This is motivated by a series of contraction properties concerning the standard Riccati equation, established by Bougerol, Liverani, Wojtkowski, Lawson, Lee and Lim: we show that some of these properties do, and that some other do not, carry over to the generalized Riccati equation. © 2014 Elsevier Inc. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Differential Equations | - |
dc.subject | Finsler metric | - |
dc.subject | Contraction rate | - |
dc.subject | Perron-Frobenius theory | - |
dc.subject | Riccati equation | - |
dc.subject | Stochastic control | - |
dc.subject | Thompson's part metric | - |
dc.title | The contraction rate in Thompson's part metric of order-preserving flows on a cone - Application to generalized Riccati equations | - |
dc.type | Article | - |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.doi | 10.1016/j.jde.2014.01.024 | - |
dc.identifier.scopus | eid_2-s2.0-84893753755 | - |
dc.identifier.volume | 256 | - |
dc.identifier.issue | 8 | - |
dc.identifier.spage | 2902 | - |
dc.identifier.epage | 2948 | - |
dc.identifier.eissn | 1090-2732 | - |
dc.identifier.isi | WOS:000331849000011 | - |
dc.identifier.issnl | 0022-0396 | - |