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Bounds on measures satisfying moment conditions

Jean B. Lasserre (lasserre***at***laas.fr)

Abstract: Given a semi algebraic set S of R^n we provide a numerical approximation procedure that yields 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 like the LMI MATLAB toolbox.

Keywords: measures; moments; positive semidefinite programming

Category 1: Applications -- Science and Engineering (Statistics )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Annals of Applied Probability 12 (2002), 1114-1137 http://projecteuclid.org/Dienst/UI/1.0/Journal?authority=euclid.aoap&issue=1031863168

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Entry Submitted: 01/17/2002
Entry Accepted: 01/17/2002
Entry Last Modified: 03/02/2003

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