Quenched Invariance Principles via Martingale Approximation
Quenched Invariance Principles via Martingale Approximation
复制标题
通过鞅近似淬灭不变性原理
DOI：
10.1007/978-1-4939-3076-0_9
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. Peligrad
中科院分区：
文献类型：
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作者：
M. Peligrad
本文综述了平稳过程和遍历过程的几乎处处中心极限定理及其函数形式。对于平稳和遍历马尔可夫链的可加泛函，这些定理在中心极限定理及其泛函形式的术语下是已知的，从一点开始。所有这些结果的共同点是它们都是通过几乎必然意义下的鞅逼近得到的。我们指出了几个应用这些结果类的混合序列，移位过程，可逆马尔可夫链，大都会黑斯廷斯算法。
In this paper we survey the almost sure central limit theorem and its functional form (quenched) for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the terminology of central limit theorem and its functional form, started at a point. All these results have in common that they are obtained via a martingale approximation in the almost sure sense. We point out several applications of these results to classes of mixing sequences, shift processes, reversible Markov chains, Metropolis Hastings algorithms.