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Zbl 1126.60070
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
Renewal processes of Mittag-Leffler and Wright type. (English)
[J] Fract. Calc. Appl. Anal. 8, No. 1, 7-38 (2005). ISSN 1311-0454; ISSN 1314-2224/e

Authors' abstract: After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely, the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore, consider corresponding renewal processes with reward and, numerically, their long-term behaviour.
[Josef Steinebach (Köln)]

MSC 2000:: *60K05 Renewal theory
26A33 Fractional derivatives and integrals (real functions)
33E12 Mittag-Leffler functions and generalizations
33E20 Functions defined by series and integrals
44A10 Laplace transform
44A35 Convolution
60G50 Sums of independent random variables
60J05 Markov processes with discrete parameter

Keywords: fractional derivative; Mittag-Leffler function; Wright function; renewal theory; Poisson process; fractional diffusion

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