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Volatility Estimation of Gaussian Ornstein–Uhlenbeck Processes of the Second Kind

Author

Listed:
  • Rachid Belfadli

    (Cadi Ayyad University)

  • Khalifa Es-Sebaiy

    (Kuwait University)

  • Fatima-Ezzahra Farah

    (Cadi Ayyad University)

Abstract

In this paper, under suitable assumptions on the Gaussian process $$G=\lbrace G_t,\,t\ge 0\rbrace $$ G = { G t , t ≥ 0 } , we establish results on uniform convergence in probability and in law stably for the realized power variation of the Riemann–Stieljes integral $$Z_t=\int _0^t u_s \text {d}Y_{s,G}^{(1)}$$ Z t = ∫ 0 t u s d Y s , G ( 1 ) with respect to $${Y_{t,G}^{(1)}}=\int _0^t \text {e}^{-s} \text {d}G_{a(s)}$$ Y t , G ( 1 ) = ∫ 0 t e - s d G a ( s ) , where u is a process of finite q-variation with $$q

Suggested Citation

  • Rachid Belfadli & Khalifa Es-Sebaiy & Fatima-Ezzahra Farah, 2023. "Volatility Estimation of Gaussian Ornstein–Uhlenbeck Processes of the Second Kind," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-17, March.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:1:d:10.1007_s10959-023-01238-9
    DOI: 10.1007/s10959-023-01238-9
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    References listed on IDEAS

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    1. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    2. Barndorff-Nielsen, Ole E. & Corcuera, José Manuel & Podolskij, Mark, 2009. "Power variation for Gaussian processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1845-1865, June.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
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