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Sub-fractional Brownian motion and its relation to occupation times

Tomasz Bojdecki (), Luis G. Gorostiza () and Anna Talarczyk ()
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Tomasz Bojdecki: Institute of Mathematics, University of Warsaw
Luis G. Gorostiza: Department of Mathematics, Centro de Investigacion y de Estudios Avanzados
Anna Talarczyk: Institute of Mathematics, University of Warsaw

No lrsp-TRS376, RePAd Working Paper Series from Département des sciences administratives, UQO

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 E (0, 2), we show how it arises from occupation time fluctuations of branching particle systems for h >= 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)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Date: 2004-06-15
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