The space-fractional Poisson process
Enzo Orsingher,Federico Polito +1 more
TLDR
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.About:
This article is published in Statistics & Probability Letters.The article was published on 2012-04-01 and is currently open access. It has received 110 citations till now. The article focuses on the topics: Fractional Poisson process & Compound Poisson process.read more
Citations
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Non-central moderate deviations for fractional Skellam processes
Jeonghwa Lee,Claudio Macci +1 more
TL;DR: In this paper , the authors present non-central moderate deviations for two fractional Skellam processes in the literature and establish that the convergences to zero are usually faster because they can prove suitable inequalities between rate functions.
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State dependent versions of the space-time fractional poisson process
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Generalized Fractional Birth Process
K. K. Kataria,M. Khandakar +1 more
TL;DR: In this paper, the generalized fractional birth process (GFBP) was introduced and a non-exploding condition for it was derived, and the system of differential equations that governs its state probabilities was obtained.
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Extended eigenvalue–eigenvector method
TL;DR: In this paper , an extension of the EEM, namely, the extended eigenvalue-eigenvector method (EEEM) is introduced which can be used to solve the linear system of fractional differential equations involving Caputo fractional derivative.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Book
Analysis of Financial Time Series
TL;DR: The author explains how the Markov Chain Monte Carlo Methods with Applications and Principal Component Analysis and Factor Models changed the way that conventional Monte Carlo methods were applied to time series analysis.
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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.
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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.
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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.