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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Central limit theorems for sums of Wick products of stationary sequences


Authors: Florin Avram and Robert Fox
Journal: Trans. Amer. Math. Soc. 330 (1992), 651-663
MSC: Primary 60F05; Secondary 60C05, 60G10
MathSciNet review: 1034656
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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).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1034656-X
PII: S 0002-9947(1992)1034656-X
Keywords: Power counting conditions, generalized Hölder inequality, generalized Szegö theorem, bond matroid, diagram formulae
Article copyright: © Copyright 1992 American Mathematical Society