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 large numbers law and a central limit theorem for this notion of expectation, we also adress the question of the convergence of the level sets of f n to the level sets of f when (f n) is a sequence of functions uniformly converging to f. We provide error estimates in terms of Hausdorff convergence. We illustrate our result on a free boundary problem.
Publié le : 2019-03-05
Classification:
Random sets,
continuity of level sets,
oriented distance functions,
large numbers law,
central limit theorem,
free boundary problem,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-02057510,
author = {Dambrine, Marc and Puig, B\'en\'edicte},
title = {Oriented distance point of view on random sets with application to shape optimization},
journal = {HAL},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-02057510}
}
Dambrine, Marc; Puig, Bénédicte. Oriented distance point of view on random sets with application to shape optimization. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-02057510/