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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Journal ArticleDOI
Fractional negative binomial and pólya processes
TL;DR: In this article, a fractional negative binomial process FNBP was defined by replacing the Poisson process by a FPP in the gamma subordinated form of the NBP.
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On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators
Khrystyna Buchak,Lyudmyla Sakhno +1 more
TL;DR: In this paper, the governing equations for marginal distributions of Poisson and Skellam processes were presented in terms of convolution-type derivatives, and the equations were given by using inverse subordinators.
Journal ArticleDOI
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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Randomly Stopped Nonlinear Fractional Birth Processes
Enzo Orsingher,Federico Polito +1 more
TL;DR: In this paper, the nonlinear classical pure birth process and the fractional pure birth processes subordinated to various random times were analyzed and the state probability distribution was derived, and the corresponding governing differential equation was presented.
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Fractional Poisson fields
Nikolai Leonenko,Ely Merzbach +1 more
TL;DR: 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.
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.
Journal ArticleDOI
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.