Large deviations and stochastic homogenization
Consider a family of probability measures \(\{\mu_ h:\) \(h\in {\mathbb{R}}\}\) on a topological vector space. If a condition ensuring tightness of the \(\mu_ h\) is satisfied, it is shown that the proof of the large deviation property in {\S} 5.1 of \textit{M. I. Freidlin} and \textit{A. D. Wentzell}, Random perturbations of dynamical systems. (1984; Zbl 0522.60055), extends to the infinite dimensional case. This result is applied to problems arising in stochastic homogenization and in connection with Donsker's invariance principle.
scientific article; zbMATH DE number 4067959