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Particle picture interpretation of some Gaussian processes related to fractional Brownian motion

Listed author(s):
  • Bojdecki, Tomasz
  • Talarczyk, Anna
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    We construct fractional Brownian motion, sub-fractional Brownian motion and negative sub-fractional Brownian motion by means of limiting procedures applied to some particle systems. These processes are obtained for full ranges of Hurst parameter.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 5 ()
    Pages: 2134-2154

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:5:p:2134-2154
    DOI: 10.1016/
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    1. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems I: Long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 1-18, January.
    2. Enriquez, Nathanaƫl, 2004. "A simple construction of the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 203-223, February.
    3. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    4. Deuschel, Jean-Dominique & Wang, Kongming, 1994. "Large deviations for the occupation time functional of a Poisson system of independent Brownian particles," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 183-209, August.
    5. Yan, Litan & Shen, Guangjun, 2010. "On the collision local time of sub-fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 296-308, March.
    6. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 19-35, January.
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