Limiting Distributions of Nonlinear Vector Functions of Stationary Gaussian Processes
Limiting Distributions of Nonlinear Vector Functions of Stationary Gaussian Processes
复制标题
平稳高斯过程非线性向量函数的极限分布
DOI：
10.1214/aop/1176990740
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发表时间：
1988
影响因子：
2.3
通讯作者：
T. Sun
中科院分区：
文献类型：
--
作者：
Hwai;T. Sun
摘要：给定一个平稳高斯向量过程x下标m， ym是Z的一个元素，以及两个实数函数H(x)和K(x)，我们定义了Z下标H上标N定义了Sum from m=1到（N -1） of Inverse a下标N和Sum from m=1到（N -1） of sub m和sub K上标K Inverse B下标N和Sum from m=1到（N -1） of sub m，其中an和Bn是适当的常数。研究了下标H上标n下标k上标k的联合极限分布。证明了H上标n和k上标k是渐近独立的，当其中一个满足中心极限定理时。讨论了这一方法在一类高斯过程的非线性无穷协调函数的极限分布中的应用。关键词：中心极限定理；九中心极限定理；远距离依赖性；平稳高斯矢量过程。
Abstract : Given a stationary Gaussian vector process x sub m, ym an element of Z, and two real functions H(x) and K(x) we define Z sub H superscript N define Sum from m=1 to (n-1) of Inverse A sub n Sum from m=1 to (n-1) of Sub m and Sub K superscript k Inverse B Sub n Sum from m=1 to (n-1) of Sub n where An and Bn are some appropriate constants. The joint limiting distribution of Sub H superscript n Sub k superscript k is investigated. It is shown that Sub H superscript n and Sub k superscript k are asymptotically independent when one of them satisfies a central limit theorem. The application of this to the limiting distribution for a certain class of non-linear infinite-coordinated functions of a Gaussian process is also discussed. Keywords: Central limit theorem; Nin-central limit theorem; Long range dependence; Stationary Gaussian vector processes.