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Tanaka formula for the fractional Brownian motion

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  • Coutin, Laure
  • Nualart, David
  • Tudor, Ciprian A.

Abstract

In this paper we find the Wiener chaos expansion for the local time of the fractional Brownian motion with Hurst parameter H and we derive a Tanaka formula in the case . As an application we deduce an Itô's formula for convex functions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:94:y:2001:i:2:p:301-315
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    References listed on IDEAS

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    1. Alòs, Elisa & Mazet, Olivier & Nualart, David, 2000. "Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 121-139, March.
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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.
    2. Shen, Guangjun & Chen, Chao, 2012. "Stochastic integration with respect to the sub-fractional Brownian motion with H∈(0,12)," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 240-251.
    3. Ehsan Azmoodeh & Lauri Viitasaari, 2015. "Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 28(1), pages 396-422, March.
    4. Tommi Sottinen & Lauri Viitasaari, 2016. "Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 29(2), pages 590-616, June.
    5. Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
    6. 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.
    7. Sun, Xichao & Yan, Litan & Yu, Xianye, 2019. "An integral functional driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2249-2285.
    8. Franco Flandoli & Peter Imkeller & Ciprian A. Tudor, 2014. "2D-Stochastic Currents over the Wiener Sheet," Journal of Theoretical Probability, Springer, vol. 27(2), pages 552-575, June.
    9. Raluca M. Balan & Ciprian A. Tudor, 2010. "Stochastic Heat Equation with Multiplicative Fractional-Colored Noise," Journal of Theoretical Probability, Springer, vol. 23(3), pages 834-870, September.
    10. Mukeru, Safari, 2017. "Representation of local times of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 1-12.
    11. Solesne Bourguin & Ciprian A. Tudor, 2012. "Asymptotic Theory for Fractional Regression Models via Malliavin Calculus," Journal of Theoretical Probability, Springer, vol. 25(2), pages 536-564, June.
    12. Bender, Christian, 2003. "An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 81-106, March.
    13. Yaskov, Pavel, 2018. "Extensions of the sewing lemma with applications," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3940-3965.
    14. Cao, Guilan & He, Kai, 2007. "Quasi-sure p-variation of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 543-548, March.

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