Fractional negative binomial and pólya processes
Palaniappan Vellai Samy,A. Maheshwari +1 more
- Vol. 38, Iss: 1, pp 77-101
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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Journal ArticleDOI
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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Book
An introduction to probability theory
TL;DR: The authors introduce probability theory for both advanced undergraduate students of statistics and scientists in related fields, drawing on real applications in the physical and biological sciences, and make probability exciting." -Journal of the American Statistical Association
Book
Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models
TL;DR: The Eulerian Functions The Bessel Functions The Error Functions The Exponential Integral Functions The Mittag-Leffler Functions The Wright Functions as mentioned in this paper The Eulerians Functions
Journal ArticleDOI
Fractional Poisson process
TL;DR: In this article, a fractional non-Markov Poisson stochastic process has been developed based on fractional generalization of the Kolmogorov-Feller equation.