Limit theorems for bifurcating integer-valued autoregressive processes

<Para ID="Par1">We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with a quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales. Copyright Springer Science+Business Media Dordrecht 2015