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Characterizations of stable laws via functional equations
Author(s) -
Gupta Arjun K.,
Jagannathan Keshav,
Nguyen Truc T.,
Shanbhag Damodar N.
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310378
Subject(s) - mathematics , generalization , divisibility rule , property (philosophy) , multivariate statistics , functional equation , function (biology) , pure mathematics , stability theorem , mathematical analysis , differential equation , statistics , cauchy distribution , philosophy , epistemology , evolutionary biology , biology
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)