  Usually the problem of drift estimation for a diffusion process is considered
under the hypothesis of ergodicity. It is less often considered under the
hypothesis of null-recurrence, simply because there are fewer limit theorems
and existing ones do not apply to the whole null-recurrent class. The aim of
this paper is to provide some limit theorems for additive functionals and
martingales of a general (ergodic or null) recurrent diffusion which would
allow us to have a somewhat unified approach to the problem of non-parametric
kernel drift estimation in the one-dimensional recurrent case. As a particular
example we obtain the rate of convergence of the Nadaraya--Watson estimator in
the case of a locally H\"{o}lder-continuous drift.
