On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields
Many statistical applications require establishing central limit theorems for sums/integrals or for quadratic forms , where is a stationary process. A particularly important case is that of Appell polynomials ( ) = ( ), ( , ) = ( , ), since the “Appell expansion rank" determines typically the type of central limit theorem...