IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i11p3940-3965.html
   My bibliography  Save this article

Extensions of the sewing lemma with applications

Author

Listed:
  • Yaskov, Pavel

Abstract

We give several extensions of the sewing lemma of Feyel and de La Pradelle and show how these results generalize Young’s integration theory in a simple and natural way. For illustrative purposes, we apply the lemma to integrals involving discontinuous functions of a fractional Brownian motion with the Hurst index H>1∕2.

Suggested Citation

  • Yaskov, Pavel, 2018. "Extensions of the sewing lemma with applications," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3940-3965.
  • Handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3940-3965
    DOI: 10.1016/j.spa.2017.09.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915300600
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2017.09.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Mishura, Yuliya & Shevchenko, Georgiy & Valkeila, Esko, 2013. "Random variables as pathwise integrals with respect to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2353-2369.
    3. Slominski, Leszek & Ziemkiewicz, Bartosz, 2005. "Inequalities for the norms of integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 79-90, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yaskov, Pavel, 2019. "On pathwise Riemann–Stieltjes integrals," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 101-107.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
    2. 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.
    3. 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.
    4. 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.
    5. Mishura, Yuliya & Shevchenko, Georgiy, 2017. "Small ball properties and representation results," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 20-36.
    6. 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.
    7. Mukeru, Safari, 2017. "Representation of local times of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 1-12.
    8. 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.
    9. 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.
    10. 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.
    11. Cao, Guilan & He, Kai, 2007. "Quasi-sure p-variation of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 543-548, March.
    12. Shi, Qun & Yu, Xianye, 2017. "Fractional smoothness of derivative of self-intersection local times," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 241-251.
    13. 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.
    14. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3940-3965. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.