IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v37y2024i1d10.1007_s10959-023-01265-6.html
   My bibliography  Save this article

Derivative of Multiple Self-intersection Local Time for Fractional Brownian Motion

Author

Listed:
  • Jingjun Guo

    (Lanzhou University of Finance and Economics)

  • Cuiyun Zhang

    (Lanzhou University of Finance and Economics)

  • Aiqin Ma

    (Lanzhou University of Finance and Economics)

Abstract

We consider existence and the Hölder continuity condition in the spatial variable for the derivative of multiple self-intersection local time for fractional Brownian motion. Moreover, under the existence condition, we study its smoothness in the sense of Meyer–Watanabe.

Suggested Citation

  • Jingjun Guo & Cuiyun Zhang & Aiqin Ma, 2024. "Derivative of Multiple Self-intersection Local Time for Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 37(1), pages 623-641, March.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:1:d:10.1007_s10959-023-01265-6
    DOI: 10.1007/s10959-023-01265-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-023-01265-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-023-01265-6?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. Nualart, David & Xu, Fangjun, 2019. "Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3981-4008.
    2. Rosen, Jay, 1986. "Tanaka's formula for multiple intersections of planar Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 131-141, October.
    3. 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.
    4. Song, Jian & Xu, Fangjun & Yu, Qian, 2019. "Limit theorems for functionals of two independent Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4791-4836.
    5. 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.
    6. Shi, Qun & Yu, Xianye, 2017. "Fractional smoothness of derivative of self-intersection local times," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 241-251.
    7. 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.
    8. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    3. Chen, Zhenlong & Xu, Peng, 2024. "Higher-order derivative of local times for space–time anisotropic Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 214(C).
    4. Bojdecki, Tomasz & Gorostiza, Luis G., 1995. "Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 191-226, December.
    5. Uemura, H., 2008. "Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1870-1891, October.
    6. 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.
    7. H. Uemura, 2004. "Tanaka Formula for Multidimensional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 17(2), pages 347-366, April.
    8. Rudenko, Alexey, 2012. "Some properties of the Itô–Wiener expansion of the solution of a stochastic differential equation and local times," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2454-2479.
    9. Rosen, Jay, 2000. "Capacitary moduli for Lévy processes and intersections," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 269-285, October.
    10. 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.
    11. Albeverio, Sergio & Hu, Yaozhong & Zhou, Xian Yin, 1997. "A remark on non-smoothness of the self-intersection local time of planar Brownian motion," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 57-65, February.
    12. Hong, Minhao & Xu, Fangjun, 2021. "Derivatives of local times for some Gaussian fields II," Statistics & Probability Letters, Elsevier, vol. 172(C).
    13. Yan, Litan & Shen, Guangjun, 2010. "On the collision local time of sub-fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 296-308, March.
    14. Jaramillo, Arturo & Nualart, David, 2017. "Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 669-700.
    15. Marie F. Kratz & José R. León, 2001. "Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields," Journal of Theoretical Probability, Springer, vol. 14(3), pages 639-672, July.
    16. Naitzat, Gregory & Adler, Robert J., 2017. "A central limit theorem for the Euler integral of a Gaussian random field," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 2036-2067.
    17. Shi, Qun & Yu, Xianye, 2017. "Fractional smoothness of derivative of self-intersection local times," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 241-251.
    18. 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.

    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:spr:jotpro:v:37:y:2024:i:1:d:10.1007_s10959-023-01265-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.