Central limit theorem for bifurcating Markov chains: the motherdaughters triangles case
Abstract
The main objective of this article is to establish a central limit theorem for additive threevariable functionals of bifurcating Markov chains. We thus extend the central limit theorem under pointwise ergodic conditions studied in BitsekiDelmas (2022) and to a lesser extent, the results of BitsekiDelmas (2022) on central limit theorem under $L^{2}$ ergodic conditions. Our results also extend and complement those of Guyon (2007) and Delmas and Marsalle (2010). In particular, when the ergodic rate of convergence is greater than $1/\sqrt{2}$, we have, for certain class of functions, that the asymptotic variance is nonzero at a speed faster than the usual central limit theorem studied by Guyon and DelmasMarsalle.
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 arXiv:
 arXiv:2207.00087
 Bibcode:
 2022arXiv220700087V
 Keywords:

 Mathematics  Probability
 EPrint:
 14 pages. arXiv admin note: text overlap with arXiv:2012.04741