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Intersection Local Time for Two Independent Fractional Brownian Motions

Author

Listed:
  • David Nualart

    (University of Kansas)

  • Salvador Ortiz-Latorre

    (Universitat de Barcelona)

Abstract

Let B H and $\widetilde{B}^{H}$ be two independent, d-dimensional fractional Brownian motions with Hurst parameter H∈(0,1). Assume d≥2. We prove that the intersection local time of B H and $\widetilde{B}^{H}$ $$I(B^{H},\widetilde{B}^{H})=\int_{0}^{T}\int_{0}^{T}\delta(B_{t}^{H}-\widetilde{B}_{s}^{H})dsdt$$ exists in L 2 if and only if Hd

Suggested Citation

  • David Nualart & Salvador Ortiz-Latorre, 2007. "Intersection Local Time for Two Independent Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 20(4), pages 759-767, December.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:4:d:10.1007_s10959-007-0106-x
    DOI: 10.1007/s10959-007-0106-x
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Jingjun Guo & Yaozhong Hu & Yanping Xiao, 2019. "Higher-Order Derivative of Intersection Local Time for Two Independent Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1190-1201, September.
    2. Junna Bi & Fangjun Xu, 2016. "A first-order limit law for functionals of two independent fractional Brownian motions in the critical case," Journal of Theoretical Probability, Springer, vol. 29(3), pages 941-957, September.
    3. Dongsheng Wu & Yimin Xiao, 2010. "Regularity of Intersection Local Times of Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 23(4), pages 972-1001, December.

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