Central limit theorem for bifurcating markov chains under L2-ergodic conditions

Autor:	S. Valère Bitseki Penda, Jean-François Delmas
Rok vydání:	2022
Předmět:	Statistics and Probability Applied Mathematics
Zdroj:	Advances in Applied Probability. 54:999-1031
ISSN:	1475-6064 0001-8678
DOI:	10.1017/apr.2022.3
Popis:	Bifurcating Markov chains (BMCs) 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 BMCs under $L^2$ -ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As an application, we study the elementary case of a symmetric bifurcating autoregressive process, which justifies the nontrivial hypothesis considered on the kernel transition of the BMCs. We illustrate in this example the phase transition observed in the fluctuations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b64f08bbdbf09b7d9098842de9c86104 https://doi.org/10.1017/apr.2022.3 Zobrazit plný text záznamu