Completness of Statistical Structures

Completness of Statistical Structures

In this survey note, we discuss the notion of completeness for statistical structures. There are at least three connections whose completeness might be taken into account, namely, the Levi-Civita connection of the given metric, the statistical connection, and its conjugate. Especially little is know...

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Main Author: Barbara Opozda
Format: Article
Language:English
Published: MDPI AG 2019-01-01
Series:Mathematics
Subjects:
statistical structure
affine hypersurface
affine sphere
conjugate symmetric statistical structure
sectional ∇-curvature
complete connection
Online Access:http://www.mdpi.com/2227-7390/7/1/104
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spelling doaj-e90c735d9c744a45bd4c93358db6258b2020-11-25T01:01:14ZengMDPI AGMathematics2227-73902019-01-017110410.3390/math7010104math7010104Completness of Statistical StructuresBarbara Opozda0Faculty of Mathematics and Computer Science, Jagiellonian University, ul. ojasiewicza 6, 30-348 Cracow, PolandIn this survey note, we discuss the notion of completeness for statistical structures. There are at least three connections whose completeness might be taken into account, namely, the Levi-Civita connection of the given metric, the statistical connection, and its conjugate. Especially little is known on the completeness of statistical connections.http://www.mdpi.com/2227-7390/7/1/104statistical structureaffine hypersurfaceaffine sphereconjugate symmetric statistical structuresectional ∇-curvaturecomplete connection
collection DOAJ
language English
format Article
sources DOAJ
author Barbara Opozda
spellingShingle Barbara Opozda
Completness of Statistical Structures
Mathematics
statistical structure
affine hypersurface
affine sphere
conjugate symmetric statistical structure
sectional ∇-curvature
complete connection
author_facet Barbara Opozda
author_sort Barbara Opozda
title Completness of Statistical Structures
title_short Completness of Statistical Structures
title_full Completness of Statistical Structures
title_fullStr Completness of Statistical Structures
title_full_unstemmed Completness of Statistical Structures
title_sort completness of statistical structures
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-01-01
description In this survey note, we discuss the notion of completeness for statistical structures. There are at least three connections whose completeness might be taken into account, namely, the Levi-Civita connection of the given metric, the statistical connection, and its conjugate. Especially little is known on the completeness of statistical connections.
topic statistical structure
affine hypersurface
affine sphere
conjugate symmetric statistical structure
sectional ∇-curvature
complete connection
url http://www.mdpi.com/2227-7390/7/1/104
work_keys_str_mv AT barbaraopozda completnessofstatisticalstructures
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