Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2458 | |
dc.contributor.author | Laschos, Vaios | |
dc.contributor.author | Mielke, Alexander | |
dc.date.accessioned | 2017-12-21T08:48:15Z | |
dc.date.available | 2019-06-28T08:10:23Z | |
dc.date.issued | 2017 | |
dc.description.abstract | By studying general geometric properties of cone spaces, we prove the existence of a distance on the space of Probability measures that turns the Hellinger--Kantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural two-parameter scaling property of the Hellinger-Kantorovich distance. For the new space, we obtain a full characterization of the geodesics. We also provide new geometric properties for the original space, including a two-parameter rescaling and reparametrization of the geodesics, local-angle condition and some partial K-semiconcavity of the squared distance, that it will be used in a future paper to prove existence of gradient flows. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2428 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2730 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2458 | |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject | Geometry on cones | eng |
dc.subject | local angle condition | eng |
dc.subject | K-semiconcavity | eng |
dc.subject | Hellinger-Kantorovich | eng |
dc.subject | Spherical Hellinger-Kantorovich | eng |
dc.subject.ddc | 510 | eng |
dc.title | Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures | eng |
dc.type | report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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