Time-changed Poisson processes of order k
TLDR
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.Abstract:
In this article, we study the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse, which we call, respectively, as TCPPoK-I and TCPPoK-II, t...read more
Citations
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Skellam type processes of order K and beyond
TL;DR: In this article, the Skellam process of order k and its running average was introduced and the marginal probabilities, Levy measures, governing difference-differential equations of the introduced processes were derived.
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Hitting probabilities of weighted Poisson processes with different intensities and their subordinations
TL;DR: In this article, the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities were studied. And the authors analyzed the hitting probability in different weights and gave an example in the case of subordination.
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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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Subordinated compound Poisson processes of order k
TL;DR: In this article, the compound Poisson processes of order $k$ (CPPoK) were introduced and its properties were discussed, using mixture of tempered stable subordinator and its right continuous inverse, the two subordinated CPPoK with various distributional properties were studied.
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Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order k and beyond
TL;DR: 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.
References
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On the long-range dependence of fractional Poisson and negative binomial processes
TL;DR: In this article, the short-range dependence (SRD) property of the increments of the fractional Poisson process was discussed, and it was shown that fractional negative binomial process (FNBP) has the same property.
Posted Content
Inverse Tempered Stable Subordinators
TL;DR: In this paper, the first-hitting time of a tempered β-stable subordinator, also called inverse tempered stable (ITS) subordinator is considered, and the limiting form of the ITS density, as the space variable $x\rightarrow 0$, and its $k$-th order derivatives are obtained.
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Subordinated diffusion and continuous time random walk asymptotics
TL;DR: In this article, the authors focus on a correspondence between CTRW and time and space fractional diffusion equation stemming from two different methods aimed to accurately approximate anomalous diffusion processes, one of them is the Monte Carlo simulation of uncoupled CTRW with a Levy α-stable distribution of jumps in space and a one-parameter Mittag-Leffler distribution of waiting times.
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Fractional Poisson fields and Martingales
TL;DR: In this paper, a martingale characterization for the Fractional Poisson process on the plane is given, and the authors extend this result to Fractionally Poisson fields, obtaining some other characterizations.
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Poisson and compound Poisson distributions of order k and some of their properties
TL;DR: In this article, a generalized compound Poisson distribution of orderk is considered, and it is shown that the sum of independent random variables, distributed according to the Poisson Law of Orderk, is distributed in the same manner.