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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,) which they call “sub-fractional Brownian motions”. The covariance function is given by

s h +t h -1 2(s+t) h +|s-t| h ,t,s0,

for a certain h(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