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On the collision local time of sub-fractional Brownian motions

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  • Yan, Litan
  • Shen, Guangjun

Abstract

Let , i=1,2, be two independent sub-fractional Brownian motions with respective indices Hi[set membership, variant](0,1). We consider the so-called collision local time where [delta] denotes the Dirac delta function. By an elementary method we show that lT is smooth in the sense of Meyer and Watanabe if and only if min{H1,H2}

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:296-308
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    References listed on IDEAS

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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. Tudor, Constantin, 2008. "Inner product spaces of integrands associated to subfractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2201-2209, October.
    3. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    4. Rosen, Jay, 1987. "The intersection local time of fractional Brownian motion in the plane," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 37-46, October.
    5. 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.
    6. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
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    Cited by:

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    3. Yu, Qian & Bajja, Salwa, 2020. "Volatility estimation of general Gaussian Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 163(C).

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