Approximation by finitely supported measures

Benoît Kloeckner

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 2, page 343-359
  • ISSN: 1292-8119

Abstract

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We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.

How to cite

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Kloeckner, Benoît. "Approximation by finitely supported measures." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 343-359. <http://eudml.org/doc/277817>.

@article{Kloeckner2012,
abstract = {We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported. },
author = {Kloeckner, Benoît},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Measures; Wasserstein distance; quantization; location problem; centroidal Voronoi tessellations; measures},
language = {eng},
month = {7},
number = {2},
pages = {343-359},
publisher = {EDP Sciences},
title = {Approximation by finitely supported measures},
url = {http://eudml.org/doc/277817},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Kloeckner, Benoît
TI - Approximation by finitely supported measures
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/7//
PB - EDP Sciences
VL - 18
IS - 2
SP - 343
EP - 359
AB - We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.
LA - eng
KW - Measures; Wasserstein distance; quantization; location problem; centroidal Voronoi tessellations; measures
UR - http://eudml.org/doc/277817
ER -

References

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