Fractional negative binomial and pólya processes
Palaniappan Vellai Samy,A. Maheshwari +1 more
- Vol. 38, Iss: 1, pp 77-101
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TLDR
In this article, a fractional negative binomial process FNBP was defined by replacing the Poisson process by a FPP in the gamma subordinated form of the NBP.Abstract:
In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Polya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.read more
Citations
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Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse
TL;DR: In this paper, the authors studied the fractional Poisson process (FPP) time-changed by an independent Levy subordinator and the inverse of the Levy subordinators, which they call TCFPP-I and TC FPP-II, respectively.
Journal ArticleDOI
Time-changed Poisson processes of order k
TL;DR: In this article, the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse was studied, which they called TCPPoK-I and TCPPoK-II.
Journal ArticleDOI
Space-fractional versions of the negative binomial and Polya-type processes
TL;DR: In this article, a space fractional negative binomial process (SFNB) was introduced by time-changing the Space fractional Poisson process by a gamma subordinator and its one-dimensional distributions were derived in terms of generalized Wright functions and their governing equations were obtained.
Journal ArticleDOI
Non-homogeneous space-time fractional Poisson processes
TL;DR: The space-time fractional Poisson process (STFPP) as mentioned in this paper is a generalization of the TFPP and the space fractional poisson process, defined by Orsingher and Poilto (2012).
Posted Content
Time-changed Poisson processes of order $k$
TL;DR: In this paper, the authors studied the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse, which they call respectively, as TCPPoK-I and TCPPOK-II, through various distributional properties, long-range dependence and limit theorems for the PPoK and the TCP-I.
References
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Journal ArticleDOI
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.
Journal ArticleDOI
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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Inverse Stable Subordinators
Mark M. Meerschaert,Peter Straka +1 more
TL;DR: This paper shows how these equations for the inverse stable subordinator can be reconciled and applications to a variety of problems in mathematics and physics.
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.