基于Keller-Liverani定理的Nagaev-Guivarc 'h方法
The Nagaev-Guivarc'h method via the Keller-Liverani theorem
摘要：
利用Nagaev-Guivarc 'h方法，通过Keller和Liverani的扰动算子定理，建立了强遍历马尔可夫链无界泛函的局部极限和Berry-Essen型定理.这种方法的主要困难是证明傅立叶核的主导特征值的泰勒展开。本文概述了这种方法，并通过证明多维局部极限定理，一阶Edgeworth展开，和多维Berry-Esseen型定理在Prohorov度量的意义下，它的扩展。当应用于一致或几何遍历链和迭代Lipschitz模型时，上述极限定理在与i.i.d.案子
英文摘要：
The Nagaev-Guivarc'h method, via the perturbation operator theorem of Keller and Liverani, has been exploited in recent papers to establish local limit and Berry-Essen type theorems for unbounded functionals of strongly ergodic Markov chains. The main difficulty of this approach is to prove Taylor expansions for the dominating eigenvalue of the Fourier kernels. This paper outlines this method and extends it by proving a multi-dimensional local limit theorem, a first-order Edgeworth expansion, and a multi-dimensional Berry-Esseen type theorem in the sense of Prohorov metric. When applied to uniformly or geometrically ergodic chains and to iterative Lipschitz models, the above cited limit theorems hold under moment conditions similar, or close, to those of the i.i.d. case.
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