×

zbMATH — the first resource for mathematics

Central limit theorem for an additive functional of the fractional Brownian motion. II. (English) Zbl 1329.60041
Summary: We prove a central limit theorem for an additive functional of the \(d\)-dimensional fractional Brownian motion with Hurst index \(H\in(\frac{1}{d+2},\frac{1}{d})\), using the method of moments, extending the result by G. C. Papanicolaou et al. [in: 1976 Duke Turbul. Conf., Durham 1976, VI.1-VI.120 (1977; Zbl 0387.60067), Reprint in: Collected papers. Volume I: Limit theorems, review articles. Edited by Rajendra Bhatia, Abhay Bhatt and K. R. Parthasarathy. Berlin: Springer; New Dehli: Hindustan Book Agency. 204–325 (2012; Zbl 1316.60097)] in the case of the standard Brownian motion.

MSC:
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
60G22 Fractional processes, including fractional Brownian motion
60J55 Local time and additive functionals
PDF BibTeX XML Cite
Full Text: DOI arXiv