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Multivariate fractional Poisson processes and compound sums

Part of: Stochastic processes Other special functions Real functions

Published online by Cambridge University Press:  19 September 2016

Luisa Beghin  and
Claudio Macci
Luisa Beghin*
Affiliation:
Sapienza Università di Roma
Claudio Macci*
Affiliation:
Università di Roma 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 Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy. Email address: [email protected]
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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.

Keywords

Conditional independenceFox‒Wright functionfractional differential equationrandom time-change

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion 60G52: Stable processes
Secondary: 26A33: Fractional derivatives and integrals 33E12: Mittag-Leffler functions and generalizations
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 3 , September 2016 , pp. 691 - 711
Copyright
Copyright © Applied Probability Trust 2016 

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