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math.ST2013★ 1 cited
A Fractional Generalization of the Poisson Processes and Some of its Properties
Nicy Sebastian, Rudolf Gorenflo
We have provided a fractional generalization of the Poisson renewal processes by replacing the first time derivative in the relaxation equation of the survival probability by a fra…
math.PR2013★ 16 cited
Laplace-Laplace analysis of the fractional Poisson process
Rudolf Gorenflo, Francesco Mainardi
We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace tra…
math.PR2013★ 16 cited
On the fractional Poisson process and the discretized stable subordinator
Rudolf Gorenflo, Francesco Mainardi
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation o…