On the convergence of generalized moments in almost sure central limit theorem期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Ildar Ibragimov Mikhail Lifshits

Affiliation:	^a St-Petersburg Branch of Steklov Mathematical Institute of Russian Academy of Sciences, 191011, Fontanka, 27, St-Petersburg, Russia ^b Mancomtech Center, 197372, Komendantskii, 22-2-49, St-Petersburg, Russia ^c U.F.R. de Mathématiques, Université de Lille I, 59655, Villeneuve d'Ascq Cedex, France

Abstract:	Let {ζ_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 ∫ hdG<∞ and a mild regularity assumption, one has a.s.

Keywords:	Almost sure limit theorems Moments Strong invariance principle
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