In this paper, we investigate a nonparametric approach to provide a recursive estimator
of the transition density of a piecewise-deterministic Markov process, from only one
observation of the path within a long time. In this framework, we do not observe a Markov
chain with transition kernel of interest. Fortunately, one may write the transition
density of interest as the ratio of the invariant distributions of two embedded chains of
the process. Our method consists in estimating these invariant measures. We state a result
of consistency and a central limit theorem under some general assumptions about the main
features of the process. A simulation study illustrates the well asymptotic behavior of
our estimator.