Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Penalized nonparametric mean square estimation of the coefficients of
  diffusion processes   We consider a one-dimensional diffusion process $(X_t)$ which is observed at
$n+1$ discrete times with regular sampling interval $\Delta$. Assuming that
$(X_t)$ is strictly stationary, we propose nonparametric estimators of the
drift and diffusion coefficients obtained by a penalized least squares
approach. Our estimators belong to a finite-dimensional function space whose
dimension is selected by a data-driven method. We provide non-asymptotic risk
bounds for the estimators. When the sampling interval tends to zero while the
number of observations and the length of the observation time interval tend to
infinity, we show that our estimators reach the minimax optimal rates of
convergence. Numerical results based on exact simulations of diffusion
processes are given for several examples of models and illustrate the qualities
of our estimation algorithms.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph