Spectral Decomposition for Generalized Domains of Semistable Attraction

Mark M. Meerschaert and Hans-Peter Scheffler

Journal of Theoretical Probability, 1997, vol. 10, issue 1, 51-71

Abstract: Abstract Suppose X, X 1 , X 2 , X 3 ,... are i.i.d. random vectors, and k n a sequence of positive integers tending to infinity in such a way that k n+1 /k n →c≥1. If there exist linear operators A n and constant vectors b n such that $$A_n (X_1 + \cdots + X_{k_n } ) - b_n $$ converges in law to some full limit, then we say that the distribution of X belongs to the generalized domain of semistable attraction of that limit law. The main result of this paper is a decomposition theorem for the norming operators A n , which allows us to reduce the problem to the case where the tail behavior of the limit law is essentially uniform in all radial directions. Applications include a complete description of moments, tails, centering, and convergence criteria.

Keywords: Operator semistable laws; generalized domains of attraction (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/A:1022638213920 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:10:y:1997:i:1:d:10.1023_a:1022638213920

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1022638213920

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().