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Donsker’s invariance principle for Lie groups. (English) Zbl 0688.60003

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 D. W. Stroock and S. R. S. Varadhan [Sankhyā, Ser. A 35, 277-294 (1973; Zbl 0299.60007)] are extremely relevant.
Reviewer: A.Mukherjea

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
60J99 Markov processes
60G10 Stationary stochastic processes
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