Geodesic
Regular Variation and the Functional Central Limit Theorem for Heavy Tailed Random Vectors
Publications de l'Institut Mathématique, _N_S_71 (2002) no. 85, p. 55

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
DOI : 10.2298/PIM0271055M
Classification : 60F17 62E20
Keywords: martingale, invariance principle, Donsker's Theorem, partial sum process, generalized domain of attraction, operator normalization 
@article{10_2298_PIM0271055M,
     author = {Mark M. Meerschaert and Steven J. Sepanski},
     title = {Regular {Variation} and the {Functional} {Central} {Limit} {Theorem} for {Heavy} {Tailed} {Random} {Vectors}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {55 },
     publisher = {mathdoc},
     volume = {_N_S_71},
     number = {85},
     year = {2002},
     doi = {10.2298/PIM0271055M},
     zbl = {1029.60019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0271055M/}
}
TY  - JOUR
AU  - Mark M. Meerschaert
AU  - Steven J. Sepanski
TI  - Regular Variation and the Functional Central Limit Theorem for Heavy Tailed Random Vectors
JO  - Publications de l'Institut Mathématique
PY  - 2002
SP  - 55 
VL  - _N_S_71
IS  - 85
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0271055M/
DO  - 10.2298/PIM0271055M
LA  - en
ID  - 10_2298_PIM0271055M
ER  - 
%0 Journal Article
%A Mark M. Meerschaert
%A Steven J. Sepanski
%T Regular Variation and the Functional Central Limit Theorem for Heavy Tailed Random Vectors
%J Publications de l'Institut Mathématique
%D 2002
%P 55 
%V _N_S_71
%N 85
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0271055M/
%R 10.2298/PIM0271055M
%G en
%F 10_2298_PIM0271055M
Mark M. Meerschaert; Steven J. Sepanski. Regular Variation and the Functional Central Limit Theorem for Heavy Tailed Random Vectors. Publications de l'Institut Mathématique, _N_S_71 (2002) no. 85, p. 55 . doi: 10.2298/PIM0271055M

Cité par Sources :