Given a semialgebraic set $S\subset \mathbb{R}^n$, we provide a numerical approximation procedure that provides upper and lower bounds on $\mu(S)$, for measures $\mu$ that satisfy some given moment conditions. The bounds are obtained as solutions of positive semidefinite programs that can be solved via standard software packages.
Publié le : 2002-08-14
Classification:
Probability,
geometric probability,
Tchebycheff bounds,
moment problem,
6008,
60D05,
90C22,
90C25
@article{1031863183,
author = {Lasserre, Jean B.},
title = {Bounds on measures satisfying moment conditions},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 1114-1137},
language = {en},
url = {http://dml.mathdoc.fr/item/1031863183}
}
Lasserre, Jean B. Bounds on measures satisfying moment conditions. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 1114-1137. http://gdmltest.u-ga.fr/item/1031863183/