Journal ArticleDOI
Fractional Poisson fields
Nikolai Leonenko,Ely Merzbach +1 more
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TLDR
Using inverse subordinators and Mittag-Leffler functions, this paper presented a new definition of a fractional Poisson process parametrized by points of the Euclidean space.Abstract:
Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space $\mathbb{R}_+^2$
. Some properties are given and, in particular, we prove a long-range dependence property.read more
Citations
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The Fractional Poisson Process and the Inverse Stable Subordinator
Ear,Nih grant R Eb +1 more
TL;DR: In this paper, 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.
Journal ArticleDOI
The fractional non-homogeneous Poisson process
TL;DR: In this article, a non-homogeneous fractional Poisson process of renewal was introduced, which replaces the time variable in the fractional poisson process with an appropriate function of time.
Journal ArticleDOI
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.
Journal ArticleDOI
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 the mixed-fractional poisson process and show that this process is the solution of a system of fractional differential-difference equations.
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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.
References
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Book
Stochastic Geometry and Its Applications
TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.
Book
Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
TL;DR: In this article, the authors present a method for computing fractional derivatives of the Fractional Calculus using the Laplace Transform Method and the Fourier Transformer Transform of fractional Derivatives.
Journal ArticleDOI
Stochastic Geometry and Its Applications.
Journal ArticleDOI
Mittag-Leffler Functions and Their Applications
TL;DR: In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented and an attempt is made to present nearly an exhaustive list of references to make the reader familiar with the present trend of research in Mittag, Leffler, and type functions and their applications.