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Correlated fractional counting processes on a finite-time interval

Part of: Other special functions Stochastic processes Distribution theory - Probability

Published online by Cambridge University Press:  30 March 2016

Luisa Beghin ,
Roberto Garra  and
Claudio Macci
Luisa Beghin*
Affiliation:
Sapienza University of Rome
Roberto Garra*
Affiliation:
Sapienza University of Rome
Claudio Macci*
Affiliation:
University of Rome Tor Vergata
*
∗Postal address: Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy. Email address: [email protected]
∗∗Postal address: Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Via A. Scarpa 16, I-00161 Roma, Italy. Email address: [email protected]
∗∗∗Postal address: Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy. Email address: [email protected]
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Abstract

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

Keywords

Poisson processnegative binomial processweighted process

MSC classification

Primary: 33E12: Mittag-Leffler functions and generalizations 60G22: Fractional processes, including fractional Brownian motion 60G55: Point processes
Secondary: 60E05: Distributions
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 1045 - 1061
Copyright
Copyright © Applied Probability Trust 2015 

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