IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i12p1463-1472.html
   My bibliography  Save this article

The rate of convergence for increments of a Brownian motion in Hölder norm

Author

Listed:
  • Liu, Yonghong
  • Li, Luoqing
  • Wan, Chenggao

Abstract

We investigate the convergence of the functional limit for increments of a Brownian motion in Hölder norm. The rate of convergence in the functional limit for increments of a d-dimensional Brownian motion is derived. The main tool in the proof is large deviation and small deviation for Brownian motion in Hölder topology.

Suggested Citation

  • Liu, Yonghong & Li, Luoqing & Wan, Chenggao, 2009. "The rate of convergence for increments of a Brownian motion in Hölder norm," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1463-1472, June.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:12:p:1463-1472
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00110-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Baldi, P. & Ben Arous, G. & Kerkyacharian, G., 1992. "Large deviations and the Strassen theorem in Hölder norm," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 171-180, August.
    2. Gao, Fuqing & Wang, Qinghua, 2005. "The rate of convergence in the functional limit theorem for increments of a Brownian motion," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 165-177, June.
    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. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    2. Hu, Yi-Jun, 1997. "A large deviation principle for small perturbations of random evolution equations in Hölder norm," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 83-99, May.
    3. Aleksandar Arandjelovi'c & Thorsten Rheinlander & Pavel V. Shevchenko, 2021. "Importance sampling for option pricing with feedforward neural networks," Papers 2112.14247, arXiv.org, revised Jun 2023.
    4. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Aug 2018.
    5. Yonghong Liu & Yongxiang Mo, 2019. "Chung’s Functional Law of the Iterated Logarithm for Increments of a Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(2), pages 721-736, June.
    6. Norvaisa, R., 1995. "The Strassen law of the iterated logarithm in Banach function spaces," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 1-8, October.
    7. Gulisashvili, Archil, 2021. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 37-79.

    More about this item

    Statistics

    Access and download statistics

    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:stapro:v:79:y:2009:i:12:p:1463-1472. 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/622892/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.