Statistical Manifold of Infinite Dimension

DOI 1 Citations 12 References

Bibliographic Information

Other Title
  • 無限次元統計多様体

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Description

This is an attempt to establish a framework of infinite dimensional information geometry. The space of the probability densikties on [0.1] which are absolutely continuous and the derivatives of which are square integrable is considered. The space is an open Hilbert manifold. The Fisher metric, however, is not compatible with the topology of the manifold. The unique existence of the covariant derivative which is metric and torsion free is proved, and the equation of the geodesic is shown. The equation is explicitly solved. It is proved that the manifold has some desirable geometrical characters.

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Details 詳細情報について

  • CRID
    1390001205768100224
  • NII Article ID
    110001883582
  • NII Book ID
    AN10367166
  • DOI
    10.11540/jsiamt.4.3_211
  • ISSN
    24240982
  • Text Lang
    ja
  • Data Source
    • JaLC
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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