Central limit theorem for bifurcating Markov chains: the mother-daughters triangles case

2022/06/30 by Penda, S. Valère Bitseki · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2207.00087

Abstract

The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in Bitseki-Delmas (2022) and to a lesser extent, the results of Bitseki-Delmas (2022) on central limit theorem under L² 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/√(2), we have, for certain class of functions, that the asymptotic variance is non-zero at a speed faster than the usual central limit theorem studied by Guyon and Delmas-Marsalle.

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