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p-variation of an integral functional driven by fractional Brownian motion

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  • Yan, Litan
  • Yang, Xiangfeng
  • Lu, Yunsheng

Abstract

Let be a one-dimensional fractional Brownian motion with Hurst parameter H[set membership, variant](0,1). We study the functionals We show that there exists a constant pH[set membership, variant](1,2) depending only on H such that the p-variation of (j=1,2) is zero if p>pH, where L1,L2 are the local time and weighted local time of BH, respectively. This extends the illustrated result for Brownian motion.

Suggested Citation

  • Yan, Litan & Yang, Xiangfeng & Lu, Yunsheng, 2008. "p-variation of an integral functional driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1148-1157, July.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1148-1157
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    References listed on IDEAS

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    1. Coutin, Laure & Nualart, David & Tudor, Ciprian A., 2001. "Tanaka formula for the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 301-315, August.
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    Cited by:

    1. Yan, Litan & Yu, Xianye & Chen, Ruqing, 2017. "Derivative of intersection local time of independent symmetric stable motions," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 18-28.
    2. Paul Jung & Greg Markowsky, 2015. "Hölder Continuity and Occupation-Time Formulas for fBm Self-Intersection Local Time and Its Derivative," Journal of Theoretical Probability, Springer, vol. 28(1), pages 299-312, March.
    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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