IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n804942.html

Remarks on Confidence Intervals for Self‐Similarity Parameter of a Subfractional Brownian Motion

Author

Listed:
  • Junfeng Liu
  • Litan Yan
  • Zhihang Peng
  • Deqing Wang

Abstract

We first present two convergence results about the second‐order quadratic variations of the subfractional Brownian motion: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we combine these results and concentration inequalities to build confidence intervals for the self‐similarity parameter associated with one‐dimensional subfractional Brownian motion.

Suggested Citation

  • Junfeng Liu & Litan Yan & Zhihang Peng & Deqing Wang, 2012. "Remarks on Confidence Intervals for Self‐Similarity Parameter of a Subfractional Brownian Motion," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:804942
    DOI: 10.1155/2012/804942
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/804942
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/804942?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
    ---><---

    References listed on IDEAS

    as
    1. Tudor, Constantin, 2008. "Inner product spaces of integrands associated to subfractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2201-2209, October.
    2. Bégyn, Arnaud, 2007. "Functional limit theorems for generalized quadratic variations of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1848-1869, December.
    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. Yuquan Cang & Junfeng Liu & Yan Zhang, 2014. "Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Kęstutis Kubilius & Dmitrij Melichov, 2016. "Exact Confidence Intervals of the Extended Orey Index for Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 785-804, September.
    3. Junfeng Liu & Zhihang Peng & Donglei Tang & Yuquan Cang, 2012. "On the Self‐Intersection Local Time of Subfractional Brownian Motion," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

    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. Bardet, Jean-Marc & Surgailis, Donatas, 2013. "Nonparametric estimation of the local Hurst function of multifractional Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1004-1045.
    2. Zhi Wang & Litan Yan, 2013. "The 𝒮‐Transform of Sub‐fBm and an Application to a Class of Linear Subfractional BSDEs," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    3. Yuquan Cang & Junfeng Liu & Yan Zhang, 2014. "Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. 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.
    5. Jingjun Guo, 2014. "Stochastic Current of Bifractional Brownian Motion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    6. 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.
    7. Junfeng Liu & Zhihang Peng & Donglei Tang & Yuquan Cang, 2012. "On the Self‐Intersection Local Time of Subfractional Brownian Motion," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

    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:wly:jnlaaa:v:2012:y:2012:i:1:n:804942. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.