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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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.

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

First available in Project Euclid: 3 October 2005

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Primary: 53D05: Symplectic manifolds, general

Fisher information metric symplectic structure Hilbert manifold probability measure


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.

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