## Electronic Communications in Probability

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

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 36, 358-371.

Dates
Accepted: 28 August 2009
First available in Project Euclid: 6 June 2016

https://projecteuclid.org/euclid.ecp/1465234745

Digital Object Identifier
doi:10.1214/ECP.v14-1487

Mathematical Reviews number (MathSciNet)
MR2535084

Zentralblatt MATH identifier
1189.60037

Rights

#### Citation

Maejima, Makoto; Nakahara, Genta. A note on new classes of infinitely divisible distributions on $\mathbb{R}^d$. Electron. Commun. Probab. 14 (2009), paper no. 36, 358--371. doi:10.1214/ECP.v14-1487. https://projecteuclid.org/euclid.ecp/1465234745

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