On structural parameter estimation of the Markov Q-process

Abstract: In the paper we consider a stochastic model which called Markov Q-processes that forms a continuous-time Markov population system. Markov Q-processes are defined as stochastic Markov branching processes with trajectories continuing in the remote future. Estimation of the structural parameter of the Markov Q-process is the main goal of this paper. To estimate this parameter, an unbiased estimator of the Lotka-Nagaev type is proposed. An asymptotic expansion of the variance of this estimator is found.