Penalized nonparametric drift estimation in a continuous time one-dimensional diffusion process

Abstract : Let $X$ be a one dimensional positive recurrent diffusion observed in continuous time. Without assuming strict stationarity of the process, we propose a nonparametric estimator of the drift function obtained by penalization. Our estimators belong to a finite-dimensional function space whose dimension is chosen according to the data. Our risk-bounds for the estimator are non-asymptotic and hold in a non-stationary regime.
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Eva Loecherbach, Dasha Loukianova, Oleg Loukianov. Penalized nonparametric drift estimation in a continuous time one-dimensional diffusion process. ESAIM: Probability and Statistics, EDP Sciences, 2011, 15, pp.197--216. ⟨10.1051/ps/2009016⟩. ⟨hal-00367993v3⟩

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