TAUBER THEORY FOR INFINITELY DIVISIBLE VARIANCE FUNCTIONS

Authors
JORGENSEN B MARTINEZ JR
Citation
B. Jorgensen et Jr. Martinez, TAUBER THEORY FOR INFINITELY DIVISIBLE VARIANCE FUNCTIONS, Bernoulli, 3(2), 1997, pp. 213-224
Citations number
24
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Bernoulli → ACNP
ISSN journal
13507265
Volume
3
Issue
2
Year of publication
1997
Pages
213 - 224
Database
ISI
SICI code
1350-7265(1997)3:2<213:TTFIDV>2.0.ZU;2-W
Abstract
We study a notion of Tauber theory for infinitely divisible natural ex ponential families, showing that the variance function of the family i s (bounded) regularly varying if and only if the canonical measure of the Levy-Khinchine representation of the family is (bounded) regularly varying. Here a variance function V is called bounded regularly varyi ng if V(mu) similar to c mu(p) either at zero or infinity, with a simi lar definition for measures. The main tool of the proof is classical T auber theory.