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

Watkins, Joseph C.

Ann. Probab. 17, No. 3, 1220-1242 (1989).

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

Keywords:

functional central limit theorem

Citations:

Zbl 0628.60018; Zbl 0299.60007