%0 Journal Article
%T Multivariate limit theorems in the context of long-range dependence
%A Murad S. Taqqu
%A Shuyang Bai
%J Mathematics
%D 2012
%I arXiv
%X 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 multivariate Gaussian process involving dependent Brownian motion marginals, or (b) a multivariate process involving dependent Hermite processes as marginals, or (c) a combination. We treat cases (a), (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.
%U http://arxiv.org/abs/1211.0576v2