Corpus ID: 235435899

Central limit theorem for bifurcating Markov chains under $L^{2}$-ergodic conditions

@inproceedings{Penda2021CentralLT,
  title={Central limit theorem for bifurcating Markov chains under \$L^\{2\}\$-ergodic conditions},
  author={S. Penda and Jean-François Delmas},
  year={2021}
}
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… Expand

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Central limit theorem for bifurcating Markov chains under pointwise ergodic conditions
  • 2021