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Fractional Poisson processes and related planar random motions

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Fractional Poisson processes and related planar random motions
2.	Creator	Author's name, affiliation, country	Luisa Beghin; Universita di Roma, La Sapienza
2.	Creator	Author's name, affiliation, country	Enzo Orsingher; Universita di Roma, La Sapienza
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Fractional derivative; Fractional heat-wave equations; Finite velocity random motions; Cylindrical waves; Random velocity motions; Compound Poisson process; Order statistics; Mittag-Leffler function
3.	Subject	Subject classification	60G55; 26A33
4.	Description	Abstract	We present three different fractional versions of the Poisson process and some related results concerning the distribution of order statistics and the compound Poisson process. The main version is constructed by considering the difference-differential equation governing the distribution of the standard Poisson process, $ N(t),t>0$, and by replacing the time-derivative with the fractional Dzerbayshan-Caputo derivative of order $\nu\in(0,1]$. For this process, denoted by $\mathcal{N}_\nu(t),t>0,$ we obtain an interesting probabilistic representation in terms of a composition of the standard Poisson process with a random time, of the form $\mathcal{N}_\nu(t)= N(\mathcal{T}_{2\nu}(t)),$ $t>0$. The time argument $\mathcal{T}_{2\nu }(t),t>0$, is itself a random process whose distribution is related to the fractional diffusion equation. We also construct a planar random motion described by a particle moving at finite velocity and changing direction at times spaced by the fractional Poisson process $\mathcal{N}_\nu.$ For this model we obtain the distributions of the random vector representing the position at time $t$, under the condition of a fixed number of events and in the unconditional case. For some specific values of $\nu\in(0,1]$ we show that the random position has a Brownian behavior (for $\nu =1/2$) or a cylindrical-wave structure (for $\nu =1$).
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2009-08-25
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/675
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-675
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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