In this paper we present nonparametric estimators for coefficients in
stochastic differential equation if the data are described by independent,
identically distributed random variables. The problem is formulated as a
nonlinear ill-posed operator equation with a deterministic forward operator
described by the Fokker-Planck equation. We derive convergence rates of the
risk for penalized maximum likelihood estimators with convex penalty terms and
for Newton-type methods. The assumptions of our general convergence results are
verified for estimation of the drift coefficient. The advantages of
log-likelihood compared to quadratic data fidelity terms are demonstrated in
Monte-Carlo simulations
