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• W2118210306 abstract "It is our intention to provide via fractional calculus a generalization of the pure and compound Poisson processes, which are known to play a fundamental role in renewal theory, without and with reward, respectively. We first recall the basic renewal theory including its fundamental concepts like waiting time between events, the survival probability, the counting function. If the waiting time is exponentially distributed we have a Poisson process, which is Markovian. However, other waiting time distributions are also relevant in applications, in particular such ones with a fat tail caused by a power law decay of its density. In this context we analyze a non-Markovian renewal process with a waiting time distribution described by the MittagLeffler function. This distribution, containing the exponential as particular case, is shown to play a fundamental role in the infinite thinning procedure of a generic renewal process governed by a power-asymptotic waiting time. We then consider the renewal theory with reward that implies a random walk subordinated to a renewal process." @default.
• W2118210306 created "2016-06-24" @default.
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• W2118210306 date "2007-01-16" @default.
• W2118210306 modified "2023-09-27" @default.
• W2118210306 title "A fractional generalization of the Poisson processes" @default.
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