著者

上林 達

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.4, no.3, pp.211-228, 1994-09-15 (Released:2017-04-08)

参考文献数

13

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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.