Abstract
Let B = {BH(t)}t≥0 be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). Consider the functionals of k independent d-dimensional fractional Brownian motions
where the Hurst index H = k/d. Using the method of moments, we prove the limit law and extending a result by Xu [19] of the case k = 1. It can also be regarded as a fractional generalization of Biane [3] in the case of Brownian motion.
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Q. Yu is partially supported by ECNU Academic Innovation Promotion Program for Excellent Doctoral Students (YBNLTS2019-010) and the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management (2018FEM-BCKYB014).
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Yu, Q. A Limit Law for Functionals of Multiple Independent Fractional Brownian Motions. Acta Math Sci 40, 734–754 (2020). https://doi.org/10.1007/s10473-020-0311-6
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DOI: https://doi.org/10.1007/s10473-020-0311-6