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Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems


 
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1. Title Title of document Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems
 
2. Creator Author's name, affiliation, country Tomasz Bojdecki; Institute of Mathematics, University of Warsaw
 
2. Creator Author's name, affiliation, country Luis G Gorostiza; Centro de Investigacion y de Estudios Avanzados, Mexico
 
2. Creator Author's name, affiliation, country Anna Talarczyk; Institute of Mathematics, University of Warsaw
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) fractional Brownian motion; weighted fractional Brownian motion; bi-fractional Brownian motion; sub-fractional Brownian motion; negative sub-fractional Brownian motion; long-range dependence; particle system
 
3. Subject Subject classification 60G18; 60J80
 
4. Description Abstract In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance $$ \int^{s\wedge t}_0 u^a [(t-u)^b+(s-u)^b]du, $$ parameters $a>-1$, $-1 < b\leq 1$, $|b|\leq 1+a$, corresponds to fractional Brownian motion for $a=0$, $-1 < b < 1$. The second one, with covariance $$ (2-h)\biggl(s^h+t^h-\frac{1}{2}[(s+t)^h +|s-t|^h]\biggr), $$ parameter $0 < h\leq 4$, corresponds to sub-fractional Brownian motion for $0 < h < 2 $. The third one, with covariance $$ -\left(s^2\log s + t^2\log t -\frac{1}{2}[(s+t)^2 \log (s+t) +(s-t)^2 \log |s-t|]\right), $$ is related to the second one. These processes come from occupation time fluctuations of certain particle systems for some values of the parameters.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) CONACyT (Mexico), MNiSW (Poland)
 
7. Date (YYYY-MM-DD) 2007-05-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1272
 
10. Identifier Digital Object Identifier 10.1214/ECP.v12-1272
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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