  In this paper we develop a statistical estimation technique to recover the
transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence
of censored data. We consider the situation where only a sub-sequence of $X$ is
available and the time gaps between the observations are iid random variables.
Under the assumption that neither the time gaps nor their distribution are
known, we provide an estimation method which applies when some transitions in
the initial Markov chain $X$ are known to be unfeasible. A consistent estimator
of $P$ is derived in closed form as a solution of a minimization problem. The
asymptotic performance of the estimator is then discussed in theory and through
numerical simulations.
