Rate of Convergence for the Weighted Hermite Variations of the Fractional Brownian Motion

Nicholas Ma () and David Nualart ()
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Nicholas Ma: The University of Kansas
David Nualart: The University of Kansas

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 1919-1947

Abstract: Abstract In this paper, we obtain a rate of convergence in the central limit theorem for high order weighted Hermite variations of the fractional Brownian motion. The proof is based on the techniques of Malliavin calculus and the quantitative stable limit theorems proved by Nourdin et al. (Ann Probab 44:1–41, 2016).

Keywords: Weighted Hermite variations; Malliavin calculus; Fractional Brownian motion; 60F05; 60H07; 60G22 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00940-x

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