| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 84 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2020007 | |
| 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,
Pau, France.
* Corresponding author: marc.dambrine@univ-pau.fr
Received:
4
February
2019
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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