A new CLT for additive functionals of Markov chains
A new CLT for additive functionals of Markov chains
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DOI：
10.1016/j.spa.2020.04.004
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发表时间：
2019-10
影响因子：
1.4
通讯作者：
M. Peligrad
中科院分区：
文献类型：
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作者：
M. Peligrad
本文研究了一般状态空间下平稳马氏链可加泛函的中心极限定理，采用了一种新的思想，即对链的过去和未来都有条件作用.实际上，我们证明了一个平稳的和完全遍历的马尔可夫链var（Sn）scinn一致有界的任何添加剂泛函，满足一个随机中心的n-中心极限定理。我们并不假设马尔可夫链是不可约的和非周期的。然而，如果马尔可夫链满足更强形式的遍历性，则不需要随机中心。在没有遍历性的情况下，分布的收敛性仍然成立，但极限分布可能不是正态分布。
In this paper we study the central limit theorem for additive functionals of stationary Markov chains with general state space by using a new idea involving conditioning with respect to both the past and future of the chain. Practically, we show that any additive functionals of a stationary and totally ergodic Markov chain with var (S n)∕ n uniformly bounded, satisfies a n− central limit theorem with a random centering. We do not assume that the Markov chain is irreducible and aperiodic. However, the random centering is not needed if the Markov chain satisfies stronger forms of ergodicity. In absence of ergodicity the convergence in distribution still holds, but the limiting distribution might not be normal.