Asymptotic results for bifurcating random coefficient autoregressive processes

Details Asymptotic results for bifurcating random coefficient autoregressive processes Asymptotic results for bifurcating random coefficient autoregressive processes

2012-04-13

arxiv.org/abs/1204.2926v1

Mathematics

Probability

arXiv admin note: substantial text overlap with arXiv:1202.0470

Scientific paper

The purpose of this paper is to study the asymptotic behavior of the weighted least square 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.

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