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Sub-fractional Brownian motion and its relation to occupation times. (English) Zbl 1076.60027
The authors study a class of centered Gaussian processes on $[0,\infty)$ which they call “sub-fractional Brownian motions”. The covariance function is given by $$ s^h + t^h -\tfrac{1}{2}\left[ (s+t)^h +\vert s-t\vert ^h\right]\;,\quad t,s\ge 0\;, $$ for a certain $h\in (0,2)$. Of course, if $h=1$, one gets the ordinary Brownian motion. Properties of those processes are stated and proved, for example, self-similarity and path properties. Finally, it is shown how those processes arise in the investigation of occupation time fluctuations of some certain particle systems.

60G15Gaussian processes
60G18Self-similar processes
60F17Functional limit theorems; invariance principles
Full Text: DOI
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