概率测度量化中的失真失配
Distortion mismatch in the quantization of probability measures
摘要：
当s>r时，我们证明了由R^d上的概率分布P的L^r最优n-量化器序列引起的L^s-量化误差的渐近性.特别地，我们证明了在自然假设下，只要s<r+d，最优速率就保持不变（并且对于紧支撑分布的情况下的每个s）。我们得到一些应用这些结果的误差界的量化为基础的积分公式在数值积分R^d和维纳空间。
英文摘要：
We elucidate the asymptotics of the L^s-quantization error induced by a sequence of L^r-optimal n-quantizers of a probability distribution P on R^d when s>r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s<r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based quadrature formulae in numerical integration on R^d and on the Wiener space.
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