Characterizations of stable laws via functional equations

✍ Scribed by Arjun K. Gupta; Keshav Jagannathan; Truc T. Nguyen; Damodar N. Shanbhag

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 159 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310378

✦ Synopsis

Abstract

In this paper, characterizations of continuous and discrete stable laws are given using Deny's Theorem. These results are obtained using infinite divisibility property of the characteristic function, and the ensueing functional equations are solved using either Deny's Theorem or the Lau–Rao Theorem. Multivariate versions of these results are also given in addition to a multidimensional generalization of the main result. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)