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Derivative of intersection local time of independent symmetric stable motions

Author

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  • Yan, Litan
  • Yu, Xianye
  • Chen, Ruqing

Abstract

Let X and X̃ be two mutually independent symmetric stable motions in R1 with respective indices α and α̃. We show that the intersection local time βt(x) of X and X̃ is differentiable in the spatial variable if α+α̃>3, and moreover we have that the p-variation of the derivative βt′(0) is zero when p>2α∨α̃α∨α̃+α+α̃−3.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:121:y:2017:i:c:p:18-28
    DOI: 10.1016/j.spl.2016.10.008
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    References listed on IDEAS

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    1. Laurent, Clément, 2010. "Large deviations for self-intersection local times of stable random walks," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2190-2211, November.
    2. 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.
    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. Shi, Qun & Yu, Xianye, 2017. "Fractional smoothness of derivative of self-intersection local times," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 241-251.

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