# Central limit theorem for bifurcating Markov chains under point-wise ergodic conditions

@inproceedings{Penda2020CentralLT, title={Central limit theorem for bifurcating Markov chains under point-wise ergodic conditions}, author={Sim'eon Valere Bitseki Penda and Jean-François Delmas}, year={2020} }

. 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 general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (2007…

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