On the Central Limit Theorem and Its Weak Invariance Principle for Strongly Mixing Sequences with Values in a Hilbert Space via Martingale Approximation
On the Central Limit Theorem and Its Weak Invariance Principle for Strongly Mixing Sequences with Values in a Hilbert Space via Martingale Approximation
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基于鞅近似的希尔伯特空间强混合序列带值的中心极限定理及其弱不变性原理
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发表时间：
2003
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通讯作者：
F. Merlevède
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作者：
F. Merlevède
本文利用伯恩斯坦分块技巧和鞅差逼近方法，将强实混合序列的一个中心极限定理推广到Hilbert空间，并作了改进.此外，我们还导出了相应的泛函中心极限定理。
In this paper we not only prove an extension to Hilbert spaces of a sharp central limit theorem for strongly real-valued mixing sequences, but also slightly improve it. The proof is mainly based on the Bernstein blocking technique and approximations by martingale differences. Moreover, we derive also the corresponding functional central limit theorem.