Non-central limit theorems for non-linear functionals of \(k\) Gaussian fields
Let \(\{X^ 1_ n\},\dots,\{X^ k_ n\}\) be stationary Gaussian processes and \(H\) be a real-valued function of \(k\) variables such that \(E(H(X^ 1_ j,\dots,X_ j^ k))=0\), \(E(H^ 2(X^ 1_ j,\dots,X^ k_ j))<\infty\) and it does not vanish on a set of positive measure. The author considers the limit behavior of the random fields \(A^{-1}_ N\sum^{(n+1)N}_{j=nN}H(X^ 1_ j,\dots,X^ k_ j)\), where \(A_ N\) are appropriate norming constants. The limit distribution is given in terms of a non-Guassian process for some \(H\).
scientific article; zbMATH DE number 168713