Distortion mismatch in the quantization of probability measures

Siegried Graf; Harald Luschgy; Gilles Pagès

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Distortion mismatch in the quantization of probability measures

Siegried Graf·Harald Luschgy·Gilles Pagès

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Abstract

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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Siegried Graf, Harald Luschgy, Gilles Pagès. 2006-02-17. Distortion mismatch in the quantization of probability measures. https://arxiv.org/abs/math/0602381

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