A note on new classes of infinitely divisible distributions on $\mathbb{R}^d$

Makoto Maejima (Keio University)
Genta Nakahara (Keio University)

Abstract


This paper introduces and studies a family of new classes of infinitely divisible distributions on $\mathbb{R}^d$ with two parameters. Depending on parameters, these classes connect the Goldie-Steutel-Bondesson class and the class of generalized type $G$ distributions, connect the Thorin class and the class $M$, connect the class $M$ and the class of generalized type $G$ distributions. These classes are characterized by stochastic integral representations with respect to Lévy processes.

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Pages: 358-371

Publication Date: August 28, 2009

DOI: 10.1214/ECP.v14-1487

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