On likelihood estimation for a discretely observed jump process

We consider the parameter estimation problem for a Markov jump process sampled at periodic epochs with a constant step. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, we provide here an explicit expression of the likelihood function of the sampled chain. Moreover under suitable ergodicity condition on the jump process, we establish the consistency and the asymptotic normality of the likelihood estimator as the observation period tends to infinity. To cite this article: D. Dehay, J.-f. Yao, C. R. Acad. Sci. Paris, Ser. I 342 (2006).