Probabilities on Simply Connected Nilpotent Lie Groups: On the Doeblin-Gnedenko Conditions for the Domain of Attraction of Stable Laws. With an Appendix on a New Proof of Siebert's Convergence Theorem for Generating Distributions

Détails

ID Serval
serval:BIB_30C921912F9B
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Probabilities on Simply Connected Nilpotent Lie Groups: On the Doeblin-Gnedenko Conditions for the Domain of Attraction of Stable Laws. With an Appendix on a New Proof of Siebert's Convergence Theorem for Generating Distributions
Périodique
International Journal of Pure and Applied Mathematics
Auteur(s)
Neuenschwander  D.
ISSN
1311-8080
Statut éditorial
Publié
Date de publication
2009
Peer-reviewed
Oui
Volume
55
Numéro
2
Pages
187-199
Langue
anglais
Résumé
The classical Doeblin-Gnedenko conditions characterizing the domain of attraction of a non-Gaussian stable law have been proved to be sufficient for completely non-Gaussian stable continuous convolution semigroups (c.c.s. for short) on simply connected nilpotent Lie groups by Carnal [2]. His method was a translation of the extreme-value-theoretic approach due to Le Page, Woodroofe, Zinn [11]. In the present note, we give a generalization of the classical proof for the sufficiency of these conditions. Together with Neuenschwander
[13] this yields the fact that in case every eigenvalue of the square matrix A has real part strictly greater than 1/2, then for a completely non-Gaussian {tA}t>0-stable (in the not necessarily strict sense) semigroup on simply connected nilpotent Lie groups, the analogue of the Doeblin-Gnedenko conditions in fact characterize the non-strict {tA}t>0-domain of attraction. We take this opportunity to state a new proof of Siebert's Convergence Theorem for c.c.s. and their generating distributions for the special case of simply connected nilpotent Lie groups and related results.
Mots-clé
stable semigroups, domains of attraction, nilpotent Lie groups, convergence of generating distributions
Création de la notice
08/02/2010 17:09
Dernière modification de la notice
21/08/2019 6:11
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