论文标题
在角度的厄尔贡条件下，对马尔可夫链分叉的中央限制定理
Central limit theorem for bifurcating Markov chains under point-wise ergodic conditions
论文作者
论文摘要
分叉马尔可夫连锁店（BMC）是马尔可夫链，由一棵完整的二元树索引，代表一个特征沿每个人都有两个孩子的人群的发展。我们为BMC的一般添加功能提供了一个中心限制定理，并证明存在三个制度。这对应于繁殖率（每个人都有两个孩子）与特征进化的成年率之间的竞争。这与Guyon（2007）的工作形成鲜明对比的是，所考虑的加性功能是Martingale增量的总和，仅出现一个制度。我们的结果可以看作是一个离散的时间版本，但是随着一般特质的演变，结果是从Adamczak和Miłoś（2015）的分支粒子系统连续设置的结果，其中特征的演变由Ornstein-Uhlenbeck过程给出。
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 general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (2007), where the considered additive functionals are sums of martingale increments, and only one regime appears. Our result can be seen as a discrete time version, but with general trait evolution, of results in the time continuous setting of branching particle system from Adamczak and Miłoś (2015), where the evolution of the trait is given by an Ornstein-Uhlenbeck process.
