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The Lévy-Lindeberg central limit theorem in Orlicz spaces $ L\sb{\Phi }$


Author: Anna T. Ławniczak
Journal: Proc. Amer. Math. Soc. 89 (1983), 673-679
MSC: Primary 60B12; Secondary 60F05, 60G17
DOI: https://doi.org/10.1090/S0002-9939-1983-0718995-5
MathSciNet review: 718995
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Abstract: An $ {L_\phi }(T,\mathcal{F},m)$-valued random element $ X$, where $ \Phi ({t^{1/2}})$ is equivalent to a concave function, satisfies the Lévy-Lindeberg central limit theorem if and only if it is centered and pre-Gaussian; that is, if and only if $ EX(t) = 0$ $ m$-a.e. and $ {\{ E{X^2}(t)\} ^{1/2}} \in {L_\phi }$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0718995-5
Keywords: Gaussian measure, Gaussian process, Orlicz space, Lévy-Lindeberg CLT
Article copyright: © Copyright 1983 American Mathematical Society