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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