A central limit theorem for nonlinear functionals of stationary Gaussian vector processes (Q1347182)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A central limit theorem for nonlinear functionals of stationary Gaussian vector processes |
scientific article; zbMATH DE number 739583
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A central limit theorem for nonlinear functionals of stationary Gaussian vector processes |
scientific article; zbMATH DE number 739583 |
Statements
A central limit theorem for nonlinear functionals of stationary Gaussian vector processes (English)
0 references
23 April 1995
0 references
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.
0 references
central limit theorem
0 references
nonlinear functionals
0 references
stationary Gaussian vector process
0 references
Hermite polynomials
0 references
