Stochastic two-scale convergence and Young measures
Probability
2021-05-27 v1 Analysis of PDEs
Abstract
In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikeli\'c and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the quenched notion of stochastic two-scale convergence (by Zhikov and Pyatnitskii). In particular, we introduce stochastic two-scale Young measures as a tool to compare mean and quenched limits. Moreover, we discuss two examples, which can be naturally analyzed via stochastic unfolding, but which cannot be treated via quenched stochastic two-scale convergence.
Cite
@article{arxiv.2105.12447,
title = {Stochastic two-scale convergence and Young measures},
author = {Martin Heida and Stefan Neukamm and Mario Varga},
journal= {arXiv preprint arXiv:2105.12447},
year = {2021}
}
Comments
30 pages. arXiv admin note: substantial text overlap with arXiv:1805.09546