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-changed Poisson processes of order $k$
TL;DR: In this paper, the authors studied the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse, which they call respectively, as TCPPoK-I and TCPPOK-II, through various distributional properties, long-range dependence and limit theorems for the PPoK and the TCP-I.
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Some probabilistic properties of fractional point processes
TL;DR: In this paper, the first hitting times of generalized Poisson processes were studied and the hitting probabilities of these processes were explicitly obtained and analyzed for the space-fractional Poisson process.
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Fractional Poisson Processes of Order k and Beyond
TL;DR: In this article, the authors introduced fractional Poisson felds of order k in n-dimensional Euclidean space and derived the marginal probabilities, governing difference-differential equations of the introduced processes.
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Convoluted Fractional Poisson Process.
K. K. Kataria,M. Khandakar +1 more
TL;DR: In this paper, the authors introduced and studied a convoluted version of the time fractional Poisson process by taking the discrete convolution with respect to space variable in the system of fractional differential equations that governs its state probabilities.
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Time-changed space-time fractional Poisson process
K. K. Kataria,M. Khandakar +1 more
TL;DR: In this paper, a time-changed version of the space-time fractional Poisson process (STFPP) by time changing it by an independent Levy subordinator with finite moments of any
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.