Asymptotic inference for continuous-time Markov chains

Summary This paper deals with asymptotic optimal inference in a time-continuous ergodic Markov chain with countable state space, based on observation of the process up to timet. Let the infinitesimal generator depend on an unknown parameter. Under weak assumptions on the parametrization, we show local asymptotic normality for the statistical model ast. As a consequence, limit distributions of sequences of competing estimators for the unknown parameter are more spread out than a specified normal distribution.