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Strong approximations for partial sums of i.i.d.B-valued r.v.'s in the domain of attraction of a Gaussian law
Authors:Uwe Einmahl
Affiliation:(1) Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-5000 Köln 41, Federal Republic of Germany
Abstract:Summary We obtain a strong approximation theorem for partial sums of i.i.d.d-dimensional r.v.'s with possibly infinite second moments. Using this result, we can extend Philipp's strong invariance principle for partial sums of i.i.d.B-valued r.v.'s satisfying the central limit theorem toB-valued r.v.'s which are only in the domain of attraction of a Gaussian law. This new strong invariance principle implies a compact as well as a functional law of the iterated logarithm which improve some recent results of Kuelbs (1985).
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