A central limit theorem for nonlinear functionals of stationary Gaussian vector processes
The author considers the limit behaviour for nonlinear functionals \[ Z^ N(H)= (\sqrt N)^{-1} \sum^ N_{j= 1} H(X_ j), \] where \(H\) is a \(d\)-dimensional function and \(X_ n= (X^ 1_ n,\dots, X^ d_ n)\) denotes a stationary Gaussian vector process, such that the correlation matrix tends fast to 0. It is shown that \(Z^ N(H)\) has a Gaussian limiting distribution.
scientific article; zbMATH DE number 739583