A functional central limit theorem for asymptotically negatively dependent random fields
A functional central limit theorem for asymptotically negatively dependent random fields
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DOI：
10.1023/a:1006720512467
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发表时间：
2000-02-01
影响因子：
0.9
通讯作者：
Zhang, LX
中科院分区：
文献类型：
--
作者：
Zhang, LX
让{X-k;k是n的一个元素，d}是一个在一定意义上渐近负相关的随机场。以通常的方式定义部分和过程，使W-n(t) = sigma(n)(-1) sigma(m小于或等于n)(X-m - EXm)，其中t是[0,1](d)的一个元素，其中sigma(n)(2) = Var （sigma(m小于或等于n) X-m）。在一些合适的条件下，我们证明了W-n（.）在分布上收敛于一个布朗表。该结果的直接结果是负相关随机场的泛函中心极限定理。该结果是基于一些关于渐近负相关随机场的一般定理，这些定理具有独立的意义。
Let {X-k; k is an element of N-d} be a random field which is asymptotically negative dependent in a certain sense. Define the partial sum process in the usual way so that W-n(t) = sigma(n)(-1) Sigma(m less than or equal to n.t)(X-m - EXm) for t is an element of [0, 1](d), where sigma(n)(2) = Var (Sigma(m less than or equal to n) X-m). Under some suitable conditions, we show that W-n(.) converges in distribution to a Brownian sheet. Direct consequences of the result are functional central limit theorems for negative dependent random fields. The result is based on some general theorems concerning asymptotically negative dependent random fields, which are of independent interest.