Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
Limit theorems for normalized sums of functions of stationary mean-zero vector-valued Gaussian sequences satisfying long range dependence conditions are considered. Depending on the rate of decay of the correlation coefficients, the limit law is either Gaussian or the law of a multiple Itô-Wiener integral. Also functional versions of these results are obtained. Furthermore, the blockwise bootstrap of these limit theorems in the case when the limit is normal could be proved. The derived limit theorems remain also true (with obvious changes) for stationary Gaussian random fields.
scientific article; zbMATH DE number 828385