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Asymptotic normality of least squares type estimators to stochastic differential equations driven by fractional Brownian motions

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  • Nakajima, Shohei
  • Shimizu, Yasutaka

Abstract

We study the problem of parametric estimation for discretely observed stochastic processes driven by fractional Brownian motion with Hurst index H∈(1/2,1). Under some assumptions on the drift coefficient, we obtain the asymptotic normality of the least square estimator of the drift parameter at special rate.

Suggested Citation

  • Nakajima, Shohei & Shimizu, Yasutaka, 2022. "Asymptotic normality of least squares type estimators to stochastic differential equations driven by fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:stapro:v:187:y:2022:i:c:s0167715222000657
    DOI: 10.1016/j.spl.2022.109476
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    References listed on IDEAS

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    1. Kohei Chiba, 2020. "An M-estimator for stochastic differential equations driven by fractional Brownian motion with small Hurst parameter," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 319-353, July.
    2. Alexandre Brouste & Marina Kleptsyna, 2010. "Asymptotic properties of MLE for partially observed fractional diffusion system," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 1-13, April.
    3. Andreas Neuenkirch & Samy Tindel, 2014. "A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 99-120, April.
    4. Liu, Yanghui & Nualart, Eulalia & Tindel, Samy, 2019. "LAN property for stochastic differential equations with additive fractional noise and continuous time observation," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2880-2902.
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