Donsker's invariance principle for Lie groups
The author establishes a functional central limit theorem for Lie groups under a mixing hypothesis. The main theorem generalizes results of Billingsley for Euclidean spaces and of the author [Probab. Theory Relat. Fields 76, 133-166 (1987; Zbl 0628.60018)] for the general linear group. In the context of this paper, the methods of \textit{D. W. Stroock} and \textit{S. R. S. Varadhan} [Sankhyā, Ser. A 35, 277-294 (1973; Zbl 0299.60007)] are extremely relevant.
scientific article; zbMATH DE number 4128140