Stochastic two-scale convergence and Young measures-Reference-Cited by-同舟云学术

Stochastic two-scale convergence and Young measures

Published:2022 Issue:2 Volume:17 Page:227
ISSN:1556-1801
Container-title:Networks and Heterogeneous Media
language:
Short-container-title:NHM

Author:

Heida Martin¹,Neukamm Stefan²,Varga Mario²

Affiliation:

1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany

2. Fakultät Mathematik, Technische Universität Dresden, 01062 Dresden, Germany

Abstract

<p style='text-indent:20px;'>In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikelić 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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability,Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability

Reference38 articles.

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