Volume 26, 2020
|Number of page(s)||24|
|Published online||27 October 2020|
Oriented distance point of view on random sets
Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP,
* Corresponding author: email@example.com
Accepted: 7 February 2020
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.
Mathematics Subject Classification: 49Q10 / 60D05
Key words: Random sets / continuity of level sets / oriented distance functions / law of large numbers / central limit theorem / free boundary problem
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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