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.
Funding
Supported in part under the Australian Research Council’s Discovery Project funding scheme (project number DP160101366) and in part by the La Trobe University DRP Grant in Mathematical and Computing Sciences.