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Higher-Order Derivative of Intersection Local Time for Two Independent Fractional Brownian Motions

Author

Listed:
  • Jingjun Guo

    (Lanzhou University of Finance and Economics)

  • Yaozhong Hu

    (University of Alberta)

  • Yanping Xiao

    (Northwest Minzu University)

Abstract

In this article, we obtain sharp conditions for the existence of the high-order derivatives (k-th order) of intersection local time $$ \widehat{\alpha }^{(k)}(0)$$ α ^ ( k ) ( 0 ) of two independent d-dimensional fractional Brownian motions $$B^{H_1}_t$$ B t H 1 and $$\widetilde{B}^{H_2}_s$$ B ~ s H 2 of Hurst parameters $$H_1$$ H 1 and $$H_2$$ H 2 , respectively. We also study their exponential integrability.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:3:d:10.1007_s10959-017-0800-2
    DOI: 10.1007/s10959-017-0800-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Jung, Paul & Markowsky, Greg, 2014. "On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3846-3868.
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    Cited by:

    1. Qian Yu, 2021. "Higher-Order Derivative of Self-Intersection Local Time for Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1749-1774, December.
    2. Qian Yu & Xianye Yu, 2024. "Limit Theorem for Self-intersection Local Time Derivative of Multidimensional Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2054-2075, September.

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