Beyond the Poisson renewal process: A tutorial survey

Authors:
Francesco Mainardi;Rudolf Gorenflo;Alessandro Vivoli
Affiliations:
Department of Physics, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy;Department of Mathematics and Informatics, Free University of Berlin, Arnimallee 2-6, D-14195 Berlin, Germany;Department of Physics, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

After sketching the basic principles of renewal theory and recalling the classical Poisson process, we discuss two renewal processes characterized by waiting time laws with the same power asymptotics defined by special functions of Mittag-Leffler and of Wright type. We compare these three processes with each other.