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Stochastic two-scale convergence and Young measures

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arxiv 2105.12447 v1 pith:GAHJXRKW submitted 2021-05-26 math.PR math.AP

Martin Heida , Stefan Neukamm , Mario Varga This is my paper · ORCID
classification math.PRmath.AP
keywords stochastictwo-scaleconvergencenotionquenchedcomparemeanmeasures
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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.

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