Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems. (English) Zbl 1128.60025 Electron. Commun. Probab. 12, 161-172 (2007). Summary: We study three self-similar, long-range dependent Gaussian processes. The first one, with covariance\[ \int_0^{s\wedge t} u^a[(t-u)^b+ (s-u)^b]\,du, \]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\[ (2-h)(s^h+t^h- \tfrac12 [(s+t)^h+|s-t|^h]), \]parameter \(0<h\leq 4\), corresponds to sub-fractional Brownian motion for \(0<h<2\). The third one, with covariance\[ -(s^2\log s+ t^2\log t- \tfrac12 [(s+t)^2\log (s+t) +(s-t)^2\log|s-t|]), \]is related to the second one. These processes come from occupation time fluctuations of certain particle systems for some values of the parameters. Cited in 1 ReviewCited in 50 Documents MSC: 60G15 Gaussian processes 60G18 Self-similar stochastic processes 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:fractional Brownian; sub-fractional Brownian motion; occupation time fluctuations PDFBibTeX XMLCite \textit{T. Bojdecki} et al., Electron. Commun. Probab. 12, 161--172 (2007; Zbl 1128.60025) Full Text: DOI arXiv EuDML