WEAK CONVERGENCE OF WEIGHTED ADDITIVE FUNCTIONALS OF LONG-RANGE DEPENDENT FIELDS

摘要

We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have the same distributions under certain assumptions. The result is applied to integrals over a multidimensional rectangle with a constant weight function.