Proceedings of the Japan Academy, Series A, Mathematical Sciences

Strong symplectic structures on spaces of probability measures with positive density function

Yuichi Shishido

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Abstract

Spaces of probability measures with positive density function on a compact Riemannian manifold are endowed with a closed 2-form associated with the Fisher information metric by using a divergence-free vector field. In this note we give a necessary and sufficient condition on the vector field that this 2-form is a strong symplectic structure.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 7 (2005), 134-136.

Dates
First available in Project Euclid: 3 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1128346018

Digital Object Identifier
doi:10.3792/pjaa.81.134

Mathematical Reviews number (MathSciNet)
MR2172604

Zentralblatt MATH identifier
1095.53054

Subjects
Primary: 53D05: Symplectic manifolds, general

Keywords
Fisher information metric symplectic structure Hilbert manifold probability measure

Citation

Shishido, Yuichi. Strong symplectic structures on spaces of probability measures with positive density function. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 7, 134--136. doi:10.3792/pjaa.81.134. https://projecteuclid.org/euclid.pja/1128346018


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