Uniform laws for stationary random functions on compact groups (Q2845218)

Uniform laws for sojourn times and the first maximum of processes with cyclic-exchangeability property are well known. The aim of this paper is to extend these assertions on properties of the standard Brownian bridge (cf. [\textit{O. Kallenberg}, Foundations of modern probability. New York, NY: Springer (1997; Zbl 0892.60001), Theorem 11.17; 2nd ed. (2002; Zbl 0996.60001)]) and results by \textit{C. Donati-Martin} et al. [Period. Math. Hung. 41, No. 1--2, 103--119 (2000; Zbl 1062.60080)] and \textit{D. Hobson} [Stat. Probab. Lett. 77, No. 2, 148--150 (2007; Zbl 1110.60077)], moreover by \textit{F. B. Knight} [in: Hommage à P. A. Meyer et J. Neveu. Paris: Société Mathématique de France. 171--187 (1996; Zbl 0867.60018)] and by \textit{L. Chaumont} et al. [Lect. Notes Math. 1755, 334--347 (2001; Zbl 0982.60020)] to the case of stationary random functions and random bridges defined on compact topological groups. The identity by Donati-Martin, Matsumoto and Yor is also extended to this case.