6533b851fe1ef96bd12a9e5d

RESEARCH PRODUCT

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

Siméon Valère Bitseki PendaJean-françois Delmas

subject

fluctuations for tree indexed Markov chain60J80[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Bifurcating Markov chains60F05binary treesbifurcating auto-regressive processdensity estimation Mathematics Subject Classification (2020): 60J05

description

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.

yearjournalcountryeditionlanguage
2021-01-01
https://hal.science/hal-03261827