Geodesic
A new strong invariance principle for sums of independent random vectors
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–2, Tome 364 (2009), pp. 5-31

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We provide a strong invariance principle for sums of independent, identically distributed random vectors which need not have finite second absolute moments. Various applications are indicated. In particular, we show how one can re-obtain some recent LIL type results from this invariance principle. Bibl. – 16 titles. 
@article{ZNSL_2009_364_a0,
     author = {U. Einmahl},
     title = {A new strong invariance principle for sums of independent random vectors},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {364},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_364_a0/}
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U. Einmahl. A new strong invariance principle for sums of independent random vectors. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–2, Tome 364 (2009), pp. 5-31. http://geodesic.mathdoc.fr/item/ZNSL_2009_364_a0/