On estimating the diffusion coefficient : parametric versus nonparametric

Marc Hoffmann

Annales de l'I.H.P. Probabilités et statistiques (2001)

  • Volume: 37, Issue: 3, page 339-372
  • ISSN: 0246-0203

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Hoffmann, Marc. "On estimating the diffusion coefficient : parametric versus nonparametric." Annales de l'I.H.P. Probabilités et statistiques 37.3 (2001): 339-372. <http://eudml.org/doc/77692>.

@article{Hoffmann2001,
author = {Hoffmann, Marc},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {adaptive estimation},
language = {eng},
number = {3},
pages = {339-372},
publisher = {Elsevier},
title = {On estimating the diffusion coefficient : parametric versus nonparametric},
url = {http://eudml.org/doc/77692},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Hoffmann, Marc
TI - On estimating the diffusion coefficient : parametric versus nonparametric
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2001
PB - Elsevier
VL - 37
IS - 3
SP - 339
EP - 372
LA - eng
KW - adaptive estimation
UR - http://eudml.org/doc/77692
ER -

References

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  1. [1] G Donhal, On estimating the diffusion coefficient, J. Appl. Probab.2 (1987) 105-114. Zbl0615.62109MR876173
  2. [2] V Genon-Catalot, J Jacod, On the estimation of the diffusion coefficient for multidimensional processes, Ann. Inst. H. Poincaré29 (1993) 119-151. Zbl0770.62070MR1204521
  3. [3] E Gobet, LAMN property for elliptic diffusions: a Malliavin calculus approach, Preprint 564, Laboratoire de Probabilités et Modèles Aléatoires, Universités Paris 6 et 7, 1999. MR1873834
  4. [4] D Florens-Zmirou, On estimating the diffusion coefficient from discrete observations, J. Appl. Probab.30 (1993) 790-804. Zbl0796.62070MR1242012
  5. [5] D.K Fuk, S.V Nagaev, Probability inequalities for sums of independent random variables, Theory Probab. Appl.4 (1971) 643-660. Zbl0259.60024
  6. [6] M Hoffmann, Lp estimation of the diffusion coefficient, Bernoulli5 (3) (1999) 447-481. Zbl0980.62073MR1693608
  7. [7] M Hoffmann, O.V Lepski, Random rates in anisotropic regression, Preprint 568, Laboratoire de Probabilités et Modèles Aléatoires, Universités Paris 6 et 7, 2000. Zbl1012.62042MR1902892
  8. [8] J Jacod, Non-parametric kernel estimation of the diffusion coefficient of a diffusion, Scand. J. Statist.27 (2000) 83-96. Zbl0938.62085MR1774045
  9. [9] J Jacod, Rates of convergence to the local time of a diffusion, Ann. I.H.P.34 (1998) 505-544. Zbl0911.60055MR1632849
  10. [10] A.P Korostelev, A.D Tsybakov, Minimax Theory of Image Reconstruction, Lecture Notes in Statistics, 82, Springer, Berlin, 1993. Zbl0833.62039MR1226450
  11. [11] O.V Lepski, How to improve accuracy of estimation, Math. Methods Statist.8 (1999) 441-486. Zbl1033.62032MR1755896
  12. [12] D Revuz, M Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991. Zbl0731.60002MR1083357

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