Asymptotic results for random coefficient bifurcating autoregressive processes

The purpose of this paper is to study the asymptotic behaviour of the weighted least-squares estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.