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On integration by parts formula and characterization of fractional Ornstein–Uhlenbeck process

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  • Sun, Xiaoxia
  • Guo, Feng

Abstract

In this paper, we consider the Ornstein–Uhlenbeck process driven by fractional Brownian motion. By showing its pull back formula, we establish the integration by parts formula for such process using the Bismut method. Conversely, we prove that such process can be characterized through its integration by parts formula.

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  • Sun, Xiaoxia & Guo, Feng, 2015. "On integration by parts formula and characterization of fractional Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 170-177.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:170-177
    DOI: 10.1016/j.spl.2015.08.023
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    References listed on IDEAS

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    1. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, November.
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    Cited by:

    1. Tommi Sottinen & Lauri Viitasaari, 2018. "Parameter estimation for the Langevin equation with stationary-increment Gaussian noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 569-601, October.
    2. Marko Voutilainen & Lauri Viitasaari & Pauliina Ilmonen & Soledad Torres & Ciprian Tudor, 2022. "Vector‐valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 992-1022, September.

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