The space-fractional Poisson process
Enzo Orsingher,Federico Polito +1 more
TLDR
In this paper, the authors introduce the space-fractional Poisson process whose state probabilities p, t, t > 0, � 2 (0,1), are governed by the equations (d/dt)pk(t) = � � (1 B)p � (t), where (B) is the fractional difference operator found in the study of time series analysis.About:
This article is published in Statistics & Probability Letters.The article was published on 2012-04-01 and is currently open access. It has received 110 citations till now. The article focuses on the topics: Fractional Poisson process & Compound Poisson process.read more
Citations
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Hilfer–Prabhakar derivatives and some applications
TL;DR: A generalization of Hilfer derivatives in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals is presented, which shows some applications in classical equations of mathematical physics such as the heat and the free electron laser equations.
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Full characterization of the fractional Poisson process
TL;DR: The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution.
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Fractional discrete processes: Compound and mixed poisson representations
Luisa Beghin,Claudio Macci +1 more
TL;DR: In this paper, two fractional versions of a family of nonnegative integer-valued processes are considered and it is shown that their probability mass functions solve fractional Kolmogorov forward equations.
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Counting processes with Bernštein intertimes and random jumps
Enzo Orsingher,Bruno Toaldo +1 more
TL;DR: In this paper, the authors considered point processes Nf(t), t > 0, with independent increments and integer-valued jumps whose distribution is expressed in terms of Bernstein functions f with Levy measure ν.
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A Generalization of the Space-Fractional Poisson Process and its Connection to some L\'evy Processes
Federico Polito,Enrico Scalas +1 more
TL;DR: In this article, a generalization of the space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form is introduced.
References
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Full characterization of the fractional Poisson process
TL;DR: The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution.
Journal ArticleDOI
Some Applications of the Fractional Poisson Probability Distribution
TL;DR: In this article, a fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers has been proposed and applied to evaluate skewness and kurtosis of the fractional Poisson probability distribution function.
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Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes
Enzo Orsingher,Federico Polito +1 more
TL;DR: In this paper, the relation between random sums and compositions of different processes is considered. But the relation is restricted to poisson processes, where the outer process is Poisson with different inner processes, and the external process is infinitely divisible.
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A fractional Poisson process in a model of dispersive charge transport in semiconductors
TL;DR: In this article, a Monte Carlo algorithm for the solution of an integro-differential equation with a fractional Poisson process is described, this method is based on appl ication of a model of the fractional poisson process.