Discrete-time Markov chains with random observation times

We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the transitions are allowed to depend on covariates. Simple and easy to update kernel estimates are proposed, and their uniform convergence rates are derived. Simulation experiments show that our estimation approach performs well.