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
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Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator
Luisa Beghin,Costantino Ricciuti +1 more
TL;DR: In this paper, the authors study non-homogeneous versions of the space-fractional and the time-frractional Poisson processes, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. The authors consider the Poisson process time-changed by H and obtain its explicit distribution and governing equation.
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Compositions of Poisson and Gamma processes
Khrystyna Buchak,Lyudmyla Sakhno +1 more
TL;DR: In this article, the authors study the models of time-changed Poisson and Skellam-type processes, where the role of time is played by compound Poisson-Gamma subordinators and their inverse (or first passage time) processes.
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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).
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Biased continuous-time random walks with Mittag-Leffler jumps
TL;DR: In this article, a space-time generalization of the Poisson process with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson Process is introduced.
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Properties of Poisson processes directed by compound Poisson-Gamma subordinators
Khrystyna Buchak,Lyudmyla Sakhno +1 more
TL;DR: In this paper, the authors consider time-changed Poisson processes where the time is expressed by compound Poisson-Gamma subordinators and derive the expressions for their hitting times.
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.