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arXiv · 1611.05585

Exact convergence order of the $L_r$-quantization error for Markov-type measures

Sanguo Zhu·Youming Zhou·Yongjian Sheng
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Abstract

Let $E$ be a graph-directed set associated with a di-graph $G$. Let $μ$ be a Markov-type measure on $E$. Assuming a separation condition for $E$, we determine the exact convergence order of the $L_r$-quantization error for $μ$. This result provides us with accurate information on the asymptotics of the quantization error, especially when the quantization coefficient is infinite.

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Sanguo Zhu, Youming Zhou, Yongjian Sheng. 2016-11-17. Exact convergence order of the $L_r$-quantization error for Markov-type measures. https://doi.org/10.1016/j.chaos.2017.03.020

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