Capture-recapture experiments with time heterogeneous capture probabilities in continuous time: A counting process approach

A martingale estimator of the size of a closed population using captures at discrete capture occasions with time heterogeneous capture probabilities is extended to experiments in continuous time. The martingale approach to the analysis of counting processes is then exploited to derive the large sample properties of the estimator. Conditions are given under which the estimator arising in the limit of discrete time capture experiments has the same asymptotic distribution as the continuous time estimator.