Computing invariant measures with the Lasserre hierarchy

Didier HenrionCentre National de la Recherche Scientifique (CNRS)Laboratoire d'Analyse et d'Architecture des Systemes (LAAS)

When a dynamical system admits an invariant measure, we show that the Lasserre hierarchy of polynomial moment-sum-of-square semidefinite relaxations can be adapted to approximate the absolutely continuous part (with respect to the Lebesgue measure) of the invariant measure with guarantees of strong convergence. We also show how the support of the singular part (continuous and discrete) of the invariant measure can be approximated arbitrary well in the Hausdorff metric.

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