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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
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