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

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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.

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Acknowledgements

The authors have been supported by Fondecyt Projects 1171335 and 1190801, and Mathamsud 19-MATH-06 and 20-MATH-05.

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Authors and Affiliations

  1. CIMFAV-INGEMAT, Universidad de Valparaiso, General Cruz 222, Valparaíso, Chile

    Karine Bertin

  2. Univ Rennes, CNRS, IRMAR – UMR 6625, 35000, Rennes, France

    Nicolas Klutchnikoff

  3. Laboratoire angevin de recherche en mathématiques (LAREMA), Université d’Angers, CNRS, 49045, Angers Cedex 01, France

    Fabien Panloup

  4. Institut de Mathématiques de Toulouse (IMT), Université de Toulouse 1 Capitole, 2 Rue du Doyen-Gabriel-Marty, 31042, Toulouse, France

    Maylis Varvenne

Authors
  1. Karine Bertin
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  2. Nicolas Klutchnikoff
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  3. Fabien Panloup
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  4. Maylis Varvenne
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Corresponding author

Correspondence to Fabien Panloup.

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Bertin, K., Klutchnikoff, N., Panloup, F. et al. Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion. Stat Inference Stoch Process 23, 271–300 (2020). https://doi.org/10.1007/s11203-020-09218-0

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  • DOI: https://doi.org/10.1007/s11203-020-09218-0

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