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title:
Constructive Quantization and Multilevel Algorithms for Quadrature of SDEs II: Random Quantization on IR^d |
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name:
Schottstedt |
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first name:
Reik
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location/conference:
SPP-JT10
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event/dateien/SPP-JT10/talks/schottstedt_eisenach.pdf |
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abstract:
In this talk we treat the approximation of a probability measure ì on
R^d, d > 2 by its empirical measure ì_N (interpreted as random quantizer) in the Wasserstein-metric. We show that the expected
p-th power (p > 0) of the Wasserstein-metric of ì and ì_N generated by N i.i.d. samples of ì
converges to zero with optimal rate N^(−p/d) as N goes to infinity. |
