Lévy–LePage Series Representation of Stable Vectors: Convergence in Variation

Content Provider	Semantic Scholar
Author	Bentkus, Vidmantas Juozulynas, Algirdas Paulauskas, Vygantas
Copyright Year	2001
Abstract	AbstractMultidimensional stable laws Gα admit a well-known Lévy–LePage series representation $$G_\alpha = \mathcal{L}\sum\limits_{j = 1}^\infty {\Gamma _j^{ - 1/\alpha } X_j } ,{\text{ 0 < }}\alpha {\text{ < 2}}$$ where Γ1, Γ2,... are the successive times of jumps of a standard Poisson process, and X1, X2,... denote i.i.d. random vectors, independent of Γ1, Γ2,.... We present (asymptotically) optimal bounds for the total variation distance between a stable law and the distribution of a partial sum of the Lévy–LePage series. In the one-dimensional case similar results were obtained earlier by Bentkus, Götze, and Paulauskas.
Starting Page	949
Ending Page	978
Page Count	30
File Format	PDF HTM / HTML
DOI	10.1023/A:1017520702943
Volume Number	14
Alternate Webpage(s)	http://www.mathematik.uni-bielefeld.de/sfb343/preprints/pr99134.ps.gz
Alternate Webpage(s)	https://doi.org/10.1023/A%3A1017520702943
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article