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Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric alpha stable processes.


 
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1. Title Title of document Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric alpha stable processes.
 
2. Creator Author's name, affiliation, country Ben M Hambly; University of Oxford
 
2. Creator Author's name, affiliation, country Liza A Jones; University of Oxford
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Number variance; symmetric alpha- stable processes; controlled variability; Gaussian fluctuations; functional limits; long memory; Gaussian processes; fractional Brownian motion
 
3. Subject Subject classification Primary 60G52, 60G15; Secondary 60F17, 15A52
 
4. Description Abstract Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct explicit new examples of processes which exhibit both divergent and saturating number variance behaviour. We derive a general expression for the number variance for the spatial particle configurations arising from these systems and this enables us to deduce various limiting distribution results for the fluctuations of the associated counting functions. In particular, knowledge of the number variance allows us to introduce and characterize a novel family of centered, long memory Gaussian processes. We obtain fractional Brownian motion as a weak limit of these constructed processes.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Second author is supported by the EPSRC through the Doctoral Training Account scheme.
 
7. Date (YYYY-MM-DD) 2007-06-13
 
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/419
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-419
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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