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Donsker's theorem for self-normalized partial sums processes

Wu, Qiying; Szyszkowicz, Barbara; Csörgő, Miklós


Let X, X1, X2,... be a sequence of nondegenerate i.i.d. random variables with zero means. In this paper we show that a self-normalized version of Donsker's theorem holds only under the assumption that X belongs to the domain of attraction of the normal law. A thus resulting extension of the arc sine law is also discussed. We also establish that a weak invariance principle holds true for self-normalized, self-randomized partial sums processes of independent random variables that are assumed to...[Show more]

CollectionsANU Research Publications
Date published: 2003
Type: Journal article
Source: The Annals of Probability
DOI: 10.1214/aop/1055425777


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