PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)Vol. 71(85), pp. 55--62 (2002)
|
|
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 VECTORSMark 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 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.
© 2003 Mathematical Institute of the Serbian Academy of Science and Arts
|