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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Competing risks and shock models governed by a generalized bivariate Poisson process
A. Di Crescenzo,Alessandra Meoli +1 more
TL;DR: In this paper , a stochastic model for the failure times of items subject to two external random shocks occurring as events in an underlying bivariate counting process is proposed, where the two kinds of shocks occur according to a bivariate space-fractional Poisson process.
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On martingale characterizations for some generalized space fractional Poisson processes
TL;DR: In this article, the authors obtained martingale characterizations for the generalized space fractional Poisson process (GSFPP) and for counting processes with Bernstein intertimes, which serve as extensions of the Watanabe's characterization for the classical homogenous Poisson processes.
Journal ArticleDOI
Skellam and time-changed variants of the generalized fractional counting process
TL;DR: In this article , the generalized fractional Skellam process (GFSP) is considered by time-changing it with an independent inverse stable subordinator, and it is observed that the GFSP is a Skellham type version of the generalized fractional counting process (GFCP), which is a fractional variant of the GCP.
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Skellam and Time-Changed Variants of the Generalized Fractional Counting Process
TL;DR: In this paper, the generalized fractional Skellam process (GFSP) is considered by time-changing it with an independent inverse stable subordinator, and its distributional properties such as the probability mass function, probability generating function, mean, variance and covariance are obtained.
Book ChapterDOI
Adomian Decomposition Method and Fractional Poisson Processes: A Survey
TL;DR: In this article, a survey of recent results related to the applications of the Adomian decomposition method (ADM) to certain fractional generalizations of the homogeneous Poisson process is given.
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.