Journal ArticleDOI
Fractional Poisson process
TLDR
In this article, a fractional non-Markov Poisson stochastic process has been developed based on fractional generalization of the Kolmogorov-Feller equation.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2003-09-01. It has received 302 citations till now. The article focuses on the topics: Fractional Poisson process & Cox process.read more
Citations
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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.
Journal ArticleDOI
Hilfer–Prabhakar derivatives and some applications
TL;DR: A generalization of Hilfer derivatives in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals is presented, which shows some applications in classical equations of mathematical physics such as the heat and the free electron laser equations.
Journal ArticleDOI
Nonergodicity of Blinking Nanocrystals and Other Levy-Walk Processes
TL;DR: Beyond blinking nanocrystals, the results describe ergodicity breaking in systems modeled by Lévy walks, for example, certain types of chaotic maps and spin dynamics to name a few.
Journal ArticleDOI
The space-fractional Poisson process
Enzo Orsingher,Federico Polito +1 more
TL;DR: In this paper, the authors introduce the space-fractional Poisson process whose state probabilities p, t, t > 0, � 2 (0,1), are governed by the equations (d/dt)pk(t) = � � (1 B)p � (t), where (B) is the fractional difference operator found in the study of time series analysis.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.