On the Convergence to Normality of Quadratic Forms in Independent Variables

Sufficient conditions are obtained for the distribution of a quadratic form of $n$ independent variables to converge to the normal distribution as $n$ increases. Particular attention is given to forms which are encountered in the theory of stationary random processes. The results of the paper are formulated in Theorems 1 and 2 of Section 4; a short description of the methods is given in Section 2.