Geodesic
On the Convergence to Normality of Quadratic Forms in Independent Variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 113-118 
P. Whittle. On the Convergence to Normality of Quadratic Forms in Independent Variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 113-118. http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a10/
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     author = {P. Whittle},
     title = {On the {Convergence} to {Normality} of {Quadratic} {Forms} in {Independent} {Variables}},
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     year = {1964},
     volume = {9},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.