Central limit theorem for bifurcating Markov chains under L²-ergodic conditions

2021/06/14 by Penda, S. Valère Bitseki, Delmas, Jean-François · 1 citation
#60F05 #60J05 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2106.07711

Abstract

Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMC under L²-ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As application, we study the elementary case of symmetric bifurcating autoregressive process, which justify the non-trivial hypothesis considered on the kernel transition of the BMC. We illustrate in this example the phase transition observed in the fluctuations.

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