Sub-fractional Brownian motion and its relation to occupation times

Tomasz Bojdecki, Luis G. Gorostiza and Anna Talarczyk

Statistics & Probability Letters, 2004, vol. 69, issue 4, 405-419

Abstract: 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.

Keywords: Long-range; dependence; Fractional; Brownian; motion; Sub-fractional; Brownian; motion; Occupation; time; fluctuations; Branching; systems (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (34)

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