We introduce a sequence of stopping times that allow to study an analogue of a life-cycle decomposition for a continuous time Markov process, which is an extension of the well-known splitting technique of Nummelin to the time-continuous case. As a consequence, we are able to give deterministic equivalents of additive functionals of the process and to state a generalisation of Chen's inequality. We apply our results to the problem of non-parametric kernel estimation of the drift of multi-dimensional recurrent, but not necessarily ergodic, diffusion processes.