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Renewal processes of Mittag-Leffler and Wright type. (English) Zbl 1126.60070

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.

MSC:

60K05 Renewal theory
26A33 Fractional derivatives and integrals
33E12 Mittag-Leffler functions and generalizations
33E20 Other functions defined by series and integrals
44A10 Laplace transform
44A35 Convolution as an integral transform
60G50 Sums of independent random variables; random walks
60J05 Discrete-time Markov processes on general state spaces
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