Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process
ESAIM: Probability and Statistics, Tome 15 (2011), pp. 197-216.

Let X be a one dimensional positive recurrent diffusion continuously observed on [0,t] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when t → ∞. The main point of our work is that we do not suppose the process to be in stationary regime neither to be exponentially β-mixing. This is possible thanks to the use of a new polynomial inequality in the ergodic theorem [E. Löcherbach, D. Loukianova and O. Loukianov, Ann. Inst. H. Poincaré Probab. Statist. 47 (2011) 425-449].

DOI : 10.1051/ps/2009016
Classification : 60F99, 60J35, 60J55, 60J60, 62G99, 62M05
Mots clés : diffusion process, adaptive estimation, regeneration method, mean square estimator, model selection, deviation inequalities
@article{PS_2011__15__197_0,
     author = {L\"ocherbach, Eva and Loukianova, Dasha and Loukianov, Oleg},
     title = {Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process},
     journal = {ESAIM: Probability and Statistics},
     pages = {197--216},
     publisher = {EDP-Sciences},
     volume = {15},
     year = {2011},
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     mrnumber = {2870512},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2009016/}
}
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Löcherbach, Eva; Loukianova, Dasha; Loukianov, Oleg. Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 197-216. doi : 10.1051/ps/2009016. http://www.numdam.org/articles/10.1051/ps/2009016/

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