On the functional CLT via martingale approximation
On the functional CLT via martingale approximation
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基于鞅近似的函数 CLT
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Peligrad
中科院分区：
文献类型：
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作者：
M. Gordin;M. Peligrad
本文给出了平稳过程部分和的鞅逼近在最大连续误差意义下有效的充要条件。这样的近似对于将条件泛函中心极限定理从鞅转移到原过程是有用的。发现的条件是简单的，很好地适应各种例子，导致更好地理解几个随机过程的结构和它们的渐近行为。这种近似方法把概率论中许多不同的例子结合在一起。它适用于由常见的投影条件（如Maxwell-Woodroofe条件）定义的变量类、各种混合过程类（包括大类强混合过程）以及具有正规或对称Markov算子的Markov链的可加泛函。
In this paper we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for transferring from the martingale to the original process the conditional functional central limit theorem. The condition found is simple and well adapted to a variety of examples, leading to a better understanding of the structure of several stochastic processes and their asymptotic behavior. The approximation brings together many disparate examples in probability theory. It is valid for classes of variables defined by familiar projection conditions such as Maxwell-Woodroofe condition, various classes of mixing processes including the large class of strongly mixing processes and for additive functionals of Markov chains with normal or symmetric Markov operators.