A central limit theorem for stationary random fields
A central limit theorem for stationary random fields
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DOI：
10.1007/s004400050153
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发表时间：
1998-03-01
影响因子：
2
通讯作者：
Dedecker, J
中科院分区：
文献类型：
--
作者：
Dedecker, J
在射影假设下，证明了严格平稳随机场的一个中心极限定理。我们的判据类似于由Gordin逼近鞅定理导出的平稳序列的射影判据。然而，我们的方法是完全不同的，因为我们采用了林德伯格的方法来建立我们的结果。它提供的判据弱于鞅类条件，并且作为一个直接的推论，我们得到了α-混合或Phi-混合随机场的中心极限定理。
We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion Is similar to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems for alpha-mixing or phi-mixing random fields.