Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using stationary processes arising in dynamical systems, followed by a discussion of the special cases of stationary processes: random processes and Diophantine processes. We are interested in how close stationary process can be to giving optimal n-means and nth optimal mean distortion errors. We also consider different ways of measuring the degree of approximation by quantization, and their advantages and disadvantages in these different contexts.

中文翻译：

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通过动态优化量化

概率分布的量化广义上是指通过有限数量的点支持的离散概率度量来估计给定的概率度量。我们考虑使用动态系统中出现的平稳过程进行量化的一般几何方法，然后讨论平稳过程的特殊情况：随机过程和丢番图过程。我们感兴趣的是平稳过程与给出最佳 n 均值和第 n 次最佳平均失真误差的接近程度。我们还考虑了通过量化来测量近似程度的不同方法，以及它们在这些不同上下文中的优缺点。