Distortion mismatch in the quantization of probability measures
Siegfried Graf, Harald Luschgy, Gilles Pagès · ESAIM Probability and Statistics · 2008
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a probability distribution P on 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 cubature formulae in numerical integration on and on the Wiener space.