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A central limit theorem for Hermitian polynomials of independent Gaussian variables

Authors:	A V Skorokhod V I Stepakhno

Institution:	(1) Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

Abstract:	The conditions of asymptotic normality of the variables $\eta _n = _{1 \leqslant i_j< ...< i, \leqslant 11}^{ \Sigma H(\delta _{lj} ,...,\delta _{ir} )}$ are studied for n and m, with H(x₁, ..., x_r) denoting Hermitian polynomials in (R^m)^r, and the ₁, ..., _n being independent Gaussian vectors in X=R^m with a zero mean and a unit correlation operator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1681–1686, December, 1990.

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