Abstract
Motivated by free boundary problems under uncertainties, we consider the oriented distance function as a way to define the expectation for a random compact or open set. In order to provide a law of large numbers and a central limit theorem for this notion of expectation, we also address the question of the convergence of the level sets of fn to the level sets of f when (fn) is a sequence of functions uniformly converging to f. We provide error estimates in term of Hausdorff convergence. We illustrate our results on a free boundary problem.
Funder
Agence Nationale de la Recherche
ISite E2S-UPPA
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
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Cited by
2 articles.
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