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December 2015 Correlated fractional counting processes on a finite-time interval
Luisa Beghin, Roberto Garra, Claudio Macci
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J. Appl. Probab. 52(4): 1045-1061 (December 2015). DOI: 10.1239/jap/1450802752

Abstract

We present some correlated fractional counting processes on a finite-timeinterval. This will be done by considering a slight generalization of theprocesses in Borges et al. (2012). The main case concerns a class ofspace-time fractional Poisson processes and, when the correlation parameter isequal to 0, the univariate distributions coincide with those of the space-timefractional Poisson process in Orsingher and Polito (2012). On the one hand,when we consider the time fractional Poisson process, the multivariatefinite-dimensional distributions are different from those presented for therenewal process in Politi et al. (2011). We also consider a caseconcerning a class of fractional negative binomial processes.

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Luisa Beghin. Roberto Garra. Claudio Macci. "Correlated fractional counting processes on a finite-time interval." J. Appl. Probab. 52 (4) 1045 - 1061, December 2015. https://doi.org/10.1239/jap/1450802752

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1337.60061
MathSciNet: MR3439171
Digital Object Identifier: 10.1239/jap/1450802752

Subjects:
Primary: 33E12, 60G22, 60G55
Secondary: 60E05

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 4 • December 2015
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