Non-central limit theorems for non-linear functional of Gaussian fields (original) (raw)

The case when the correlation function r(n)=EXoX, tends slowly to 0 is investigated. In this situation the norming constants A N tend to infinity more rapidly than the usual norming sequence As= ~. Also the limit may be a non-Gaussian process. The results are generalized to the case when the parameter-set is multi-dimensional. * This paper contains results closely connected to those of the paper by Taqqu, Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 53-83 (1979), The investigations were done independently and at about the same time. Different methods were used