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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 1, Pages 116–140
DOI: https://doi.org/10.4213/tvp842 (Mi tvp842) 		 
This article is cited in 14 scientific papers (total in 14 papers)

A curious example from statistical differential geometry

G. Kallianpur, Y.-T. Kim
Full-text PDF (948 kB) Citations (14)
DOI: https://doi.org/10.4213/tvp842
Abstract: We consider an example of a family of probability measures on an infinite dimensional space which are mutually singular. Although the Fisher information metric and its variants are not available, it is shown that the parameter manifold has a natural differential structure that is non-Riemannian with nonzero curvature. It is also shown that there is no Riemannian metric compatible with the natural affine connection for which the curvature is not zero.
Keywords: stochastic partial differential equation, parameter manifold, affine connection, non-Riemannian geometry.
Received: 13.03.1996
English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 1, Pages 42–62
DOI: https://doi.org/10.1137/S0040585X97976659
Bibliographic databases:
Language: Russian
Citation: G. Kallianpur, Y.-T. Kim, “A curious example from statistical differential geometry”, Teor. Veroyatnost. i Primenen., 43:1 (1998), 116–140; Theory Probab. Appl., 43:1 (1999), 42–62
Citation in format AMSBIB
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\by G.~Kallianpur, Y.-T.~Kim
\paper A curious example from statistical differential geometry
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 1
\pages 116--140
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1669992}
\zmath{https://zbmath.org/?q=an:0963.62003}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 1
\pages 42--62
\crossref{https://doi.org/10.1137/S0040585X97976659}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000079809600004}
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  • https://doi.org/10.4213/tvp842
  • https://www.mathnet.ru/eng/tvp/v43/i1/p116
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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