Gnedenko-type limit theorems for cyclostationary \(c^2\)-processes
Let \(X_1(t), \ldots ,X_n(t)\), \(t\in (-\infty,\infty)\), be independent copies of a Gaussian zero-mean cyclostationary process \(X(t)\). Set \({\mathbb X}(t)=(X_1(t),X_2(t), \ldots ,X_n(t))\). Under various additional assumptions, the authors prove that the limit distributions of affinely transformed maxima \({\max(\| {\mathbb X}(t)\| , t\in[0,T]})\), as \(t \to \infty\), are the Gumbel distribution.
scientific article; zbMATH DE number 2108231