Sub-fractional Brownian motion and its relation to occupation times
AbstractWe 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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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 69 (2004)
Issue (Month): 4 (October)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Shen, Guangjun & Chen, Chao, 2012. "Stochastic integration with respect to the sub-fractional Brownian motion with H∈(0,12)," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 240-251.
- Slominski, Leszek & Ziemkiewicz, Bartosz, 2009. "On weak approximations of integrals with respect to fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 543-552, February.
- Bojdecki, Tomasz & Talarczyk, Anna, 2012. "Particle picture interpretation of some Gaussian processes related to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2134-2154.
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