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Pré-Publication, Document De Travail Année : 2015

Lebesgue decomposition in action via semidefinite relaxations

Résumé

Given all (finite) moments of two measures $\mu$ and $\lambda$ on $\R^n$, we provide a numerical scheme to obtain the Lebesgue decomposition $\mu=\nu+\psi$ with $\nu\ll\lambda$ and $\psi\perp\lambda$. When $\nu$ has a density in $L_\infty(\lambda)$ then we obtain two sequences of finite moments vectors of increasing size (the number of moments) which converge to the moments of $\nu$ and $\psi$ respectively, as the number of moments increases. Importantly, {\it no} \`a priori knowledge on the supports of $\mu, \nu$ and $\psi$ is required.
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Dates et versions

hal-01212385 , version 1 (06-10-2015)
hal-01212385 , version 2 (25-01-2016)

Identifiants

Citer

Jean-Bernard Lasserre. Lebesgue decomposition in action via semidefinite relaxations. 2015. ⟨hal-01212385v1⟩
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