Journal of Applied Probability

Fractional discrete processes: compound and mixed Poisson representations

Luisa Beghin and Claudio Macci

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider two fractional versions of a family of nonnegative integer-valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As particular examples in this family, we can define fractional versions of some processes in the literature as the Pólya-Aeppli process, the Poisson inverse Gaussian process, and the negative binomial process. We also define and study some more general fractional versions with two fractional parameters.

Article information

Source
J. Appl. Probab., Volume 51, Number 1 (2014), 19-36.

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771411

Digital Object Identifier
doi:10.1239/jap/1395771411

Mathematical Reviews number (MathSciNet)
MR3189439

Zentralblatt MATH identifier
1294.26004

Subjects
Primary: 26A33: Fractional derivatives and integrals 33E12: Mittag-Leffler functions and generalizations 60G22: Fractional processes, including fractional Brownian motion

Keywords
Cox process doubly stochastic Poisson process negative binomial process Pólya-Aeppli process Poisson inverse Gaussian process

Citation

Beghin, Luisa; Macci, Claudio. Fractional discrete processes: compound and mixed Poisson representations. J. Appl. Probab. 51 (2014), no. 1, 19--36. doi:10.1239/jap/1395771411. https://projecteuclid.org/euclid.jap/1395771411


Export citation