On a Szego Type Limit Theorem, the Holder-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 of functions of 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 satisfied by these functionals. We review and extend here to multidimensional indices a functional analysis approach to this problem proposed by Avram and Brown (1989), based on the method of cumulants and on integrability assumptions in the spectral domain; several applications are presented as well. 
Florin Avram (LMA-PAU), Nikolai Leonenko, Ludmila Sakhno