PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 71(85), pp. 55--62 (2002)
REGULAR VARIATION AND THE FUNCTIONAL CENTRAL LIMIT THEOREM FOR HEAVY TAILED RANDOM VECTORS
Mark M. Meerschaert and Steven J. SepanskiDepartment of Mathematics, University of Nevada, Reno, NV 89557-0045 and Department of Mathematical Sciences, Saginaw Valley State University, University Center, MI 48710
Abstract: 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
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Electronic fulltext finalized on: 19 Feb 2003. This page was last modified: 20 Feb 2003.
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