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Projection estimators of the stationary density of a differential equation driven by the fractional Brownian motion

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  • Marie, Nicolas

Abstract

The paper deals with projection estimators of the density of the stationary solution X to a differential equation driven by the fractional Brownian motion under a dissipativity condition on the drift function. A model selection method is provided and, thanks to the concentration inequality for Lipschitz functionals of discrete samples of X proved in Bertin et al. (2020), an oracle inequality is established for the adaptive estimator.

Suggested Citation

  • Marie, Nicolas, 2022. "Projection estimators of the stationary density of a differential equation driven by the fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s0167715221002066
    DOI: 10.1016/j.spl.2021.109244
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    References listed on IDEAS

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    1. 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.
    2. Claire Lacour & Pascal Massart & Vincent Rivoirard, 2017. "Estimator Selection: a New Method with Applications to Kernel Density Estimation," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 298-335, August.
    3. Karine Bertin & Nicolas Klutchnikoff & Fabien Panloup & Maylis Varvenne, 2020. "Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 271-300, July.
    4. Fabienne Comte & Nicolas Marie, 2019. "Nonparametric estimation in fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 359-382, October.
    5. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
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