Hooke’s law in statistical manifolds and divergences
Hooke’s law in statistical manifolds and divergences
复制标题
统计流形和散度中的胡克定律
DOI：
10.1017/s002776300000739x
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发表时间：
2000
影响因子：
0.8
通讯作者：
R. Kobayashi
中科院分区：
文献类型：
--
作者：
Masayuki Henmi;R. Kobayashi
利用对偶仿射坐标系之间的勒让德变换，定义了对偶平坦统计流形的正则发散的概念。在这篇文章中，我们引入了一个新的两点函数定义的任何三元组（g，，*）的黎曼度量g和两个仿射连接和 *。我们表明，这解释了典型的分歧，而不使用特殊的坐标（对偶仿射坐标）的存在，但在只有经典力学方面的关于？-和？*-测地线。我们还讨论了两点函数的性质，并表明这与定义在对偶平坦统计流形上的正则散度具有一些重要的性质。
The concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two point function defined for any triple (g,∇, ∇*) of a Riemannian metric g and two affine connections ∇ and ∇*. We show that this interprets the canonical divergence without refering to the existence of special coordinates (dual affine coordinates) but in terms of only classical mechanics concerning ∇- and ∇*-geodesics. We also discuss the properties of the two point function and show that this shares some important properties with the canonical divergence defined on dually flat statistical manifolds.