How many processes have Poisson counts?

Timothy C. Brown and Aihua Xia

Stochastic Processes and their Applications, 2002, vol. 98, issue 2, 331-339

Abstract: The Poisson process has the well-known Poisson count property: the count of points in any subset of the carrier space has a Poisson distribution. To specify the complete distribution of a point process it is necessary and sufficient to specify all of the joint distributions of the counts of points in any (finite disjoint) collection of bounded sets in the carrier space. Suppose that only the Poisson count property is specified for a random collection of points. We reveal the circumstances in which the Poisson count property does indeed determine the distribution. Curiously, there is a 'phase transition' in this property with the boundary being mean measures having 2 atoms.

Keywords: Point; process; Poisson; process; Finite; dimensional; distribution; Probability; generating; function; Phase; transition (search for similar items in EconPapers)
Date: 2002
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(01)00150-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:98:y:2002:i:2:p:331-339

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().