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Parameter estimation for the complex fractional Ornstein–Uhlenbeck processes with Hurst parameter H∈(0,12)

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  • Alazemi, Fares
  • Alsenafi, Abdulaziz
  • Chen, Yong
  • Zhou, Hongjuan

Abstract

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein–Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen et al. (2017) to the case of Hurst parameter H∈(14,12) and the results of Hu et al. (2019) to a two-dimensional case. When H∈(0,14], it is found that the integrand of the estimator is not in the domain of the standard divergence operator. To facilitate the proofs, we develop a new inner product formula for functions of bounded variation in the reproducing kernel Hilbert space of fractional Brownian motion with Hurst parameter H∈(0,12). This formula is also applied to obtain the second moments of the so-called α-order fractional Brownian motion and the α-fractional bridges with the Hurst parameter H∈(0,12).

Suggested Citation

  • Alazemi, Fares & Alsenafi, Abdulaziz & Chen, Yong & Zhou, Hongjuan, 2024. "Parameter estimation for the complex fractional Ornstein–Uhlenbeck processes with Hurst parameter H∈(0,12)," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924011081
    DOI: 10.1016/j.chaos.2024.115556
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    References listed on IDEAS

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    1. Yaozhong Hu & David Nualart & Hongjuan Zhou, 2019. "Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 111-142, April.
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