On local asymptotic normality for birth and death on a flow

We consider statistical models for birth and death on a flow and prove local asymptotic normality as the observation time approaches infinity; as a consequence, we know how to characterize asymptotically efficient estimators for the unknown parameter. We construct a sequence of minimum distance estimators based on observed death positions which is strongly consistent and asymptotically normal, and improve it to get an efficient estimator for a parameter present in the death rate function.