Tudor, Ciprian A. Hsu-Robbins and Spitzer’s theorems for the variations of fractional Brownian motion. (English) Zbl 1189.60085 Electron. Commun. Probab. 14, 278-289 (2009). Summary: Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein’s method, we prove P. L. Hsu and H. Robbins’ [Proc. Natl. Acad. Sci. USA 33, 25–31 (1947; Zbl 0030.20101)] and F. Spitzer’s [Trans. Am. Math. Soc. 82, 323–339 (1956; Zbl 0071.13003)] theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion. Cited in 1 Document MSC: 60G22 Fractional processes, including fractional Brownian motion 60H05 Stochastic integrals 60F05 Central limit and other weak theorems 60H07 Stochastic calculus of variations and the Malliavin calculus Keywords:multiple stochastic integrals; selfsimilar processes; fractional Brownian motion; hermite processes; limit theorems; Stein’s method Citations:Zbl 0030.20101; Zbl 0071.13003 PDFBibTeX XMLCite \textit{C. A. Tudor}, Electron. Commun. Probab. 14, 278--289 (2009; Zbl 1189.60085) Full Text: DOI arXiv EuDML EMIS