Optimal quantizers for Radon random vectors in a Banach space

Details Optimal quantizers for Radon random vectors in a Banach space Optimal quantizers for Radon random vectors in a Banach space

2005-04-12

arxiv.org/abs/math/0504236v1

Mathematics

Probability

Scientific paper

For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e\_{n,r}(X,E) = inf{(E (\min\_{a \in \alpha} || X-a ||^r)^{1/r}}, where the infimum is taken over all subsets \alpha of E with card(\alpha) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.

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