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On the convergence of generalized moments in almost sure central limit theorem

Let {[zeta]k} be the normalized sums corresponding to a sequence of i.i.d. variables with zero mean and unit variance. Define random measures and let G be the normal distribution. We show that for each continuous function h satisfying [integral operator] hdG<[infinity] and a mild regularity assumption, one has a.s.
Year of publication:
1998
Authors: Ibragimov, Ildar ; Lifshits, Mikhail
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 40.1998, 4, p. 343-351
Publisher: Elsevier
Keywords: Almost sure limit theorems Moments Strong invariance principle
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10005224057
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