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@article{ECP1272,
	author = {Tomasz Bojdecki and Luis Gorostiza and Anna Talarczyk},
	title = {Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {12},
	year = {2007},
	keywords = {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},
	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.},
	pages = {no. 17, 161-172},
	issn = {1083-589X},
	doi = {10.1214/ECP.v12-1272},    
        url = {http://ecp.ejpecp.org/article/view/1272}}