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Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion

Author

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  • Karine Bertin

    (Universidad de Valparaiso)

  • Nicolas Klutchnikoff

    (Univ Rennes, CNRS, IRMAR – UMR 6625)

  • Fabien Panloup

    (Université d’Angers, CNRS)

  • Maylis Varvenne

    (Université de Toulouse 1 Capitole, 2 Rue du Doyen-Gabriel-Marty)

Abstract

We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary regime.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:2:d:10.1007_s11203-020-09218-0
    DOI: 10.1007/s11203-020-09218-0
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    References listed on IDEAS

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    1. Castellana, J. V. & Leadbetter, M. R., 1986. "On smoothed probability density estimation for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 179-193, February.
    2. Yu. Kutoyants, 1998. "Efficient Density Estimation for Ergodic Diffusion Processes," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 131-155, May.
    3. M. Mishra & B. Prakasa Rao, 2011. "Nonparametric estimation of trend for stochastic differential equations driven by fractional Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 101-109, May.
    4. Comte, F. & Merlevède, F., 2005. "Super optimal rates for nonparametric density estimation via projection estimators," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 797-826, May.
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    Cited by:

    1. 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).

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