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Sub-fractional Brownian motion and its relation to occupation times



We study a long-range dependence Gaussian process which we call "sub-fractional Brownian motion" (sub-fBm), because it is intermediate between Brownian motion (Bm) and fractional Brownian motion (fBm) in the sense that it has properties analogous to those of fBm, but the increments on non-overlapping intervals are more weakly correlated and their covariance decays polynomially at a higher rate. Sub-fBm has a parameter h[set membership, variant](0,2), we show how it arises from occupation time fluctuations of branching particle systems for h[greater-or-equal, slanted]1 and we exhibit the long memory effect of the initial condition.

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