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

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  • Nicholas Ma

    (The University of Kansas)

  • David Nualart

    (The University of Kansas)

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).

Suggested Citation

  • Nicholas Ma & David Nualart, 2020. "Rate of Convergence for the Weighted Hermite Variations of the Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1919-1947, December.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:4:d:10.1007_s10959-019-00940-x
    DOI: 10.1007/s10959-019-00940-x
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    References listed on IDEAS

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    1. Ivan Nourdin & David Nualart, 2010. "Central Limit Theorems for Multiple Skorokhod Integrals," Journal of Theoretical Probability, Springer, vol. 23(1), pages 39-64, March.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Andreas Neuenkirch & Ivan Nourdin, 2007. "Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 20(4), pages 871-899, December.
    4. Rumen L. Mishkov, 2000. "Generalization of the formula of Faa di Bruno for a composite function with a vector argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
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    Cited by:

    1. Levental, S. & Vellaisamy, P., 2023. "Formulas for the divergence operator in isonormal Gaussian space," Statistics & Probability Letters, Elsevier, vol. 194(C).

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