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
More filters
Posted Content
On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators
Khrystyna Buchak,Lyudmyla Sakhno +1 more
TL;DR: In this article, 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
Hitting probabilities of weighted Poisson processes with different intensities and their subordinations
TL;DR: In this article, the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities were studied. And the authors analyzed the hitting probability in different weights and gave an example in the case of subordination.
Journal ArticleDOI
Generalized Fractional Counting Process
TL;DR: The generalized fractional counting process (GFCP) was introduced and studied by Di Crescenzo et al. as discussed by the authors , and its covariance structure is studied, using which its long-range dependence property is established.
Journal ArticleDOI
On Distributions of Certain State Dependent Fractional Point Processes
TL;DR: In this paper, the explicit expressions for the state probabilities of various state dependent fractional point processes were obtained by employing the Adomian decomposition method to solve the difference differential equations governing state probabilities.
Journal ArticleDOI
Generalized Counting Processes in a Stochastic Environment
Davide Cocco,Massimiliano Giona +1 more
TL;DR: This paper addresses the generalization of counting processes through the age formalism of Lévy Walks, providing several examples and applications and showing the occurrence of new phenomena related to the modulation of the long-term scaling exponent by environmental noise.
References
More filters
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.