Generalized Szegő theorems and asymptotics of cumulants by graphical methods

Avram, Florin

doi:10.1090/S0002-9947-1992-1059708-X

Generalized Szegő theorems and asymptotics of cumulants by graphical methods
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by Florin Avram PDF

Trans. Amer. Math. Soc. 330 (1992), 637-649 Request permission

Abstract:

We obtain some general asymptotics results about a class of deterministic sums called "sums with dependent indices," which generalize a classical theorem of Szegö. The above type of sums is encountered when establishing convergence to the Gaussian distribution of sums of Wick products by the method of cumulants. Our asymptotic results reduce in this situation the proof of the central limit theorem to the study of the connectivity of a family of associated graphs.

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