Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order k and beyond
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In this paper, a fractional non-homogeneous Poisson Poisson process of order k and polya-aeppli Poisson Process of order K were characterized by deriving their non-local governing equations.Abstract:
We introduce two classes of point processes: a fractional non-homogeneous Poisson process of order k and a fractional non-homogeneous Polya-Aeppli process of order k: We characterize these processes by deriving their non-local governing equations. We further study the covariance structure of the processes and investigate the long-range dependence property.read more
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Generalized Fractional Counting Process
TL;DR: The generalized fractional counting process (GFCP) was introduced and studied by Di Crescenzo et al. as discussed by the authors , and its covariance structure is studied, using which its long-range dependence property is established.
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Generalized Fractional Counting Process
K. K. Kataria,M. Khandakar +1 more
TL;DR: The generalized fractional counting process (GFCP) was introduced and studied by Di Crescenzo et al. as mentioned in this paper, and its covariance structure is studied using which its long-range dependence property is established.
References
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The Fractional Poisson Process and the Inverse Stable Subordinator
TL;DR: In this article, it was shown that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional poisson process with Mittag-Leffler waiting times, which unifies the two main approaches in stochastic theory of time-fractional diffusion equations.
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Fractional Poisson processes and related planar random motions
Luisa Beghin,Enzo Orsingher +1 more
TL;DR: In this article, three different fractional versions of the standard Poisson process and some related results concerning the distribution of order statistics and the compound poisson process are presented, and a planar random motion described by a particle moving at finite velocity and changing direction at times spaced by fractional Poisson processes is presented.
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A generalized geometric distribution and some of its properties
TL;DR: In this article, a generalized geometric distribution is introduced and briefly studied, and sufficient conditions are presented under which we can derive the limiting distribution of Yr - kr as r → ∞.
Journal Article
A fractional generalization of the Poisson processes
TL;DR: In this article, a non-Markovian renewal process with a waiting time distribution described by the Mittag-Leffler function is analyzed, and it is shown that this distribution plays a fundamental role in the infinite thinning procedure of a generic renewal process governed by a power asymptotic waiting time.
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Poisson-type processes governed by fractional and higher-order recursive differential equations
Luisa Beghin,Enzo Orsingher +1 more
TL;DR: In this article, the authors considered some fractional extensions of the recursive differential equation governing the Poisson process, i.e. the generalized Mittag-Leffler functions.