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March 2014 Fractional discrete processes: compound and mixed Poisson representations
Luisa Beghin, Claudio Macci
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J. Appl. Probab. 51(1): 19-36 (March 2014). DOI: 10.1239/jap/1395771411

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.

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Luisa Beghin. Claudio Macci. "Fractional discrete processes: compound and mixed Poisson representations." J. Appl. Probab. 51 (1) 19 - 36, March 2014. https://doi.org/10.1239/jap/1395771411

Information

Published: March 2014
First available in Project Euclid: 25 March 2014

zbMATH: 1294.26004
MathSciNet: MR3189439
Digital Object Identifier: 10.1239/jap/1395771411

Subjects:
Primary: 26A33, 33E12, 60G22

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 1 • March 2014
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