Tauber theory for infinitely divisible variance functions

Jørgensen, Bent; Raúl Martínez, José

Bernoulli, Tome 3 (1997) no. 3, p. 213-224 / Harvested from Project Euclid

Résumé

We study a notion of Tauber theory for infinitely divisible natural exponential families, showing that the variance function of the family is (bounded) regularly varying if and only if the canonical measure of the Lévy-Khinchine representation of the family is (bounded) regularly varying. Here a variance function V is called bounded regularly varying if V(μ)\sim cμ^p either at zero or infinity, with a similar definition for measures. The main tool of the proof is classical Tauber theory.

Publié le : 1997-06-14
Classification: exponential dispersion model, Lévy-Khinchine representation, Lévy measure, natural exponential family, regular variation, Tweedie family

@article{1177526729,
     author = {J\o rgensen, Bent and Ra\'ul Mart\'\i nez, Jos\'e},
     title = {Tauber theory for infinitely divisible variance functions},
     journal = {Bernoulli},
     volume = {3},
     number = {3},
     year = {1997},
     pages = { 213-224},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177526729}
}

Jørgensen, Bent; Raúl Martínez, José. Tauber theory for infinitely divisible variance functions. Bernoulli, Tome 3 (1997) no. 3, pp.  213-224. http://gdmltest.u-ga.fr/item/1177526729/