4 research outputs found
Branching Markov processes and related asymptotics
AbstractModels 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
Random coefficients bifurcating autoregressive processes
This paper presents a model of asymmetric bifurcating autoregressive process
with random coefficients. We couple this model with a Galton Watson tree to
take into account possibly missing observations. We propose least-squares
estimators for the various parameters of the model and prove their consistency
with a convergence rate, and their asymptotic normality. We use both the
bifurcating Markov chain and martingale approaches and derive new important
general results in both these frameworks