## Advances in Applied Probability

- Adv. in Appl. Probab.
- Volume 48, Number 3 (2016), 691-711.

### Multivariate fractional Poisson processes and compound sums

Luisa Beghin and Claudio Macci

#### Abstract

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (nonfractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

#### Article information

**Source**

Adv. in Appl. Probab., Volume 48, Number 3 (2016), 691-711.

**Dates**

First available in Project Euclid: 19 September 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.aap/1474296310

**Mathematical Reviews number (MathSciNet)**

MR3568887

**Zentralblatt MATH identifier**

1351.60045

**Subjects**

Primary: 60G22: Fractional processes, including fractional Brownian motion 60G52: Stable processes

Secondary: 26A33: Fractional derivatives and integrals 33E12: Mittag-Leffler functions and generalizations

**Keywords**

Conditional independence Fox‒Wright function fractional differential equation random time-change

#### Citation

Beghin, Luisa; Macci, Claudio. Multivariate fractional Poisson processes and compound sums. Adv. in Appl. Probab. 48 (2016), no. 3, 691--711. https://projecteuclid.org/euclid.aap/1474296310