CENTRAL LIMIT-THEOREMS FOR NON-LINEAR FUNCTIONALS OF GAUSSIAN FIELDS
CENTRAL LIMIT-THEOREMS FOR NON-LINEAR FUNCTIONALS OF GAUSSIAN FIELDS
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DOI：
10.1016/0047-259x(83)90019-2
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发表时间：
1983-01-01
影响因子：
1.6
通讯作者：
MAJOR, P
中科院分区：
文献类型：
--
作者：
BREUER, P;MAJOR, P
本文证明了对于平稳高斯场的某些非线性泛函，如果相关函数足够快地趋于零，则中心极限定理成立。结果制定的Hermite秩的功能和相关函数的速度。然后，我们展示了一个例子，当极限场是自相似和高斯，但不一定由独立的元素。
In the present paper it is shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero. The results are formulated in terms of the Hermite rank of the functional and of the rate of the correlation function. Then we show an example when the limit field is self-similar and Gaussian but not necessarily consisting of independent elements.