Gradient systems associated with probability distributions
Gradient systems associated with probability distributions
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与概率分布相关的梯度系统
DOI：
10.1007/bf03167211
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发表时间：
1994
影响因子：
0.9
通讯作者：
Yoshimasa Nakamura
中科院分区：
文献类型：
--
作者：
Yoshimasa Nakamura
给出了不同概率分布流形上的梯度系统。结果表明，梯度系统可以通过勒让德变换线性化。由此推论，流形上的相应流以指数方式收敛到势函数的平衡点。证明了偶数维流形上的梯度系统是完全可积的哈密顿系统。特别地，高斯分布的梯度系统允许Lax对表示。
Gradient systems on manifolds of various probability distributions are presented. It is shown that the gradient systems can be linearized by the Legendre transformation. It follows that the corresponding flows on the manifolds converge to equilibrium points of potential functions exponentially. It is proved that gradient systems on manifolds of even dimensions are completely integrable Hamiltonian systems. Especially, the gradient system for the Gaussian distribution admits a Lax pair representation.