PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 71(85), pp. 5562 (2002) 

REGULAR VARIATION AND THE FUNCTIONAL CENTRAL LIMIT THEOREM FOR HEAVY TAILED RANDOM VECTORSMark M. Meerschaert and Steven J. SepanskiDepartment of Mathematics, University of Nevada, Reno, NV 895570045 and Department of Mathematical Sciences, Saginaw Valley State University, University Center, MI 48710Abstract: Multivariable regular variation is used, along with the martingale central limit theorem, to give a very simple proof that the partial sum process for a sequence of independent, identically distributed random vectors converges to a Brownian motion whenever the summands belong to the generalized domain of attraction of a normal law. This includes the heavy tailed case, where the covariance matrix is undefined because some of the marginals have infinite variance. Keywords: martingale; invariance principle; Donsker's Theorem; partial sum process; generalized domain of attraction; operator normalization Classification (MSC2000): 60F17; 62E20 Full text of the article:
Electronic fulltext finalized on: 19 Feb 2003. This page was last modified: 20 Feb 2003.
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