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
Generalized Counting Process: its Non-Homogeneous and Time-Changed Versions
TL;DR: In this paper , a nonhomogeneous generalized counting process (NGCP) was introduced, which is a generalized fractional counting process with a non-homogeneous stable subordinator.
Journal ArticleDOI
Tempered space fractional negative binomial process
TL;DR: In this paper , the authors defined a tempered space fractional negative binomial process (TSFNBP) by replacing the Poisson process by a tempered Space fractional Poisson Process (TSFPP) in the gamma subordinated form of the NBP and studied its distributional properties, long-range dependence property and its connection with pde's.
Poisson processes with jumps governed by lower incomplete gamma subordinator and its variations
TL;DR: In this paper , the authors studied the Poisson process time-changed by independent L'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma sub-subordinator, and tempered incomplete gamma super-sub-subdominator.
Posted Content
Multivariate fractional Poisson processes and compound sums
Luisa Beghin,Claudio Macci +1 more
TL;DR: In this paper, the authors presented multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) poisson processes.
Posted Content
Asymmetric random walks with bias generated by discrete-time counting processes
TL;DR: In this article, a new class of asymmetric random walks on the one-dimensional infinite lattice is introduced, where the direction of the jumps (positive or negative) is determined by a discrete-time renewal process which is independent of the unit jumps.
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.