Free Access
Volume 15, 2011
Page(s) 197 - 216
Published online 05 January 2012
  1. G. Banon, Nonparametric identification for diffusion processes. SIAM J. Control. Optim. 16 (1978) 380–395. [CrossRef] [MathSciNet] [Google Scholar]
  2. Y. Baraud, F. Comte and G. Viennet, Adaptive estimation in autoregression or β-mixing regression via model selection. Ann. Stat. 29 (2001) 839–875. [CrossRef] [Google Scholar]
  3. Y. Baraud, F. Comte and G. Viennet, Model selection for (auto-)regression with dependent data. ESAIM: P&S 5 (2001) 33–49. [Google Scholar]
  4. A. Barron, L. Birgé and P. Massart, Risks bounds for model selection via penalization. Prob. Th. Rel. Fields 113 (1999) 301–413. [Google Scholar]
  5. F. Comte, V. Genon-Catalot and Y. Rozenholc, Penalized nonparametric mean square estimation of the coefficients of diffusion processes. Bernoulli 13 (2007) 514–543. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Dalalyan, Sharp adaptive estimation of the drift function for ergodic diffusions. Ann. Stat. 33 (2005) 507–2528. [Google Scholar]
  7. A.S. Dalalyan and Yu.A. Kutoyants, Asymptotically efficient trend coefficient estimation for ergodic diffusion. Math. Meth. Stat. 11 (2002) 402–427. [Google Scholar]
  8. S. Delattre, M. Hoffmann and M. Kessler, Dynamics adaptive estimation of a scalar diffusion. Prpublication PMA-762, Univ. Paris 6 (2002). Available at Mathematical Reviews (MathSciNet): MR1895888 Project Euclid: [Google Scholar]
  9. L. Galtchouk and S. Pergamenschikov, Sequential nonparametric adaptive estimation of the drift coefficient in the diffusion processes. Math. Meth. Stat. 10 (2001) 316–330. [Google Scholar]
  10. M. Hoffmann, Adaptive estimation in diffusion processes. Stochastic Processes Appl. 79 (1999) 135–163. [Google Scholar]
  11. Yury A. Kutoyants, Statistical inference for ergodic diffusion processes. Springer Series in Statistics. London: Springer (2004). [Google Scholar]
  12. O. Lepskii, One problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl. 35 (1999) 459–470. [Google Scholar]
  13. G.G. Lorentz, M. von Golitschek and Y. Makovoz, Constructive approximation: advanced problems. Grundlehren der Mathematischen Wissenschaften 304. Berlin: Springer (1996). [Google Scholar]
  14. D. Loukianova and O. Loukianov, Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions. Ann. Inst. Henri Poincaré 44 (2008) 771–786. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Löcherbach and D. Loukianova, On Nummelin splitting for continuous time Harris recurrent Markov processes and application to kernel estimation for multi-dimensional diffusions. Stoch. Proc. Appl. 118 (2008) 301–1321. [Google Scholar]
  16. E. Löcherbach, D. Loukianova and O. Loukianov, Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011) 425–449. [Google Scholar]
  17. T.D. Pham, Nonparametric estimation of the drift coefficient in the diffusion equation. Math. Operationsforsch. Statist., Ser. Statistics 1 (1981) 61–73. [Google Scholar]
  18. B.L.S. Prakasa Rao, Statistical Inference for Diffusion Type Processes. London: Edward Arnold. MR1717690 (1999) [Google Scholar]
  19. D. Revuz and M. Yor, Continuous martingales and Brownian motion. 3rd ed. Grundlehren der Mathematischen Wissenschaften 293. Berlin: Springer (2005). [Google Scholar]
  20. V.G. Spokoiny, Adaptive drift estimation for nonparametric diffusion model. Ann. Stat. 28 (2000) 815–836. [Google Scholar]
  21. A.Yu. Veretennikov, On polynomial mixing bounds for stochastic differential equations. Stoch. Proc. Appl. 70 (1997) 115–127. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.