Branching Markov processes and related asymptotics

Models for Markov processes indexed by a branching process are presented. The new class of models is referred to as the branching Markov process (BMP). The law of large numbers and a central limit theorem for the BMP are established. Bifurcating autoregressive processes (BAR) are special cases of the general BMP model discussed in the paper. Applications to parameter estimation are also presented.