Central limit theorems for sums of Wick products of stationary sequences

Abstract

We show, by the method of cumulants, that checking whether the central limit theorem for sums of Wick powers of a stationary sequence holds can be reduced to the study of an associated graph problem (see Corollary 1). We obtain thus central limit theorems under various integrability conditions on the cumulant spectral functions (Theorems 2, 3).