论文标题
分叉马尔可夫链的中央限制定理：母女三角案例
Central limit theorem for bifurcating Markov chains: the mother-daughters triangles case
论文作者
论文摘要
本文的主要目的是建立一个分叉马尔可夫链的添加剂三变量函数的中心限制定理。因此，我们在Bitseki-Delmas（2022）研究的点上延长了中心极限定理，在$ l^{2} $ ergodic条件下，Bitseki-Delmas（2022）的结果在较小程度上，Bitseki-Delmas（2022）的结果。我们的结果还扩展并补充了Guyon（2007）和Delmas and Marsalle（2010）的结果。特别是，当沿着趋同的趋同速率大于$ 1/\ sqrt {2} $时，对于某些类别的功能，我们拥有比Guyon和Delmas-Marsalle研究的常规中央定理的渐近方差并不快。
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 $L^{2}$ 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 non-zero at a speed faster than the usual central limit theorem studied by Guyon and Delmas-Marsalle.
