We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of...

For a continuous-time Markov process, commonly, only discrete-time observations are available. We analyze multiple observations of a homogeneous Markov jump process with an absorbing state. We establish consistency of the maximum likelihood estimator, as the number of Markov processes increases....