MULTIVARIATE LIMIT THEOREMS IN THE CONTEXT OF LONG-RANGE DEPENDENCE

被引:25
作者
Bai, Shuyang [1 ]
Taqqu, Murad S. [1 ]
机构
[1] Boston Univ, Boston, MA 02215 USA
关键词
Long-range dependence; Gaussian process; central limit theorems; non-central limit theorems; asymptotic independence; multiple Wiener-Ito integrals; NONLINEAR FUNCTIONALS; INDEPENDENCE;
D O I
10.1111/jtsa.12046
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting limit law may be (a) a multi-variate Gaussian process involving dependent Brownian motion marginals, (b) a multi-variate process involving dependent Hermite processes as marginals or (c) a combination. We treat cases (a) and (b) in general and case (c) when the Hermite components involve ranks 1 and 2. We include a conjecture about case (c) when the Hermite ranks are arbitrary, although the conjecture can be resolved in some special cases.
引用
收藏
页码:717 / 743
页数:27
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