# Central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models

@inproceedings{Penda2021CentralLT, title={Central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models}, 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. Motivated by the functional estimation of the density of the invariant probability measure which appears as the asymptotic distribution of the trait, we prove the consistence and the Gaussian fluctuations for a kernel estimator of this density based on late generations. In this setting, it is interesting to note that the… Expand

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Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains models

- Mathematics
- 2021

Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by proving a moderate… Expand

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