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Pré-Publication, Document De Travail Année : 2021

Central limit theorem for bifurcating Markov chains under L 2 -ergodic conditions

Résumé

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 L 2-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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Dates et versions

hal-03261827 , version 1 (16-06-2021)

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  • HAL Id : hal-03261827 , version 1

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Siméon Valère Bitseki Penda, Jean-François Delmas. Central limit theorem for bifurcating Markov chains under L 2 -ergodic conditions. 2021. ⟨hal-03261827⟩
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