IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v13y2000i3d10.1023_a1007854310936.html
   My bibliography  Save this article

An Isometric Approach to Generalized Stochastic Integrals

Author

Listed:
  • Yulia Mishura

    (Kiev University)

  • Esko Valkeila

    (University of Helsinki)

Abstract

The possibility to extend the classical Ito's construction of stochastic integrals is studied. This construction can be applied to fractional Brownian motions with Hurst index H∈(0, 1/2). A change of variables formula for fractional Brownian motions in terms of the stochastic integrals is given.

Suggested Citation

  • Yulia Mishura & Esko Valkeila, 2000. "An Isometric Approach to Generalized Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 13(3), pages 673-693, July.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:3:d:10.1023_a:1007854310936
    DOI: 10.1023/A:1007854310936
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1007854310936
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1007854310936?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. Novikov, Alexander & Valkeila, Esko, 1999. "On some maximal inequalities for fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 47-54, August.
    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. Yan, Litan, 2004. "Maximal inequalities for the iterated fractional integrals," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 69-79, August.
    2. Wood, Andrew T. A., 2001. "Acknowledgement of priority," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 349-349, June.
    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.
    4. Michael J. Klass & Ming Yang, 2012. "Maximal Inequalities for Additive Processes," Journal of Theoretical Probability, Springer, vol. 25(4), pages 981-1012, December.
    5. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    6. Lee, Chihoon, 2012. "Bounds on exponential moments of hitting times for reflected processes on the positive orthant," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1120-1128.
    7. Dorival Le~ao & Alberto Ohashi & Francesco Russo, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part I," Papers 1707.05234, arXiv.org, revised Jun 2019.
    8. Orimar Sauri, 2024. "Asymptotic Error Distribution of the Euler Scheme for Fractional Stochastic Delay Differential Equations with Additive Noise," Papers 2402.08513, arXiv.org.
    9. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    10. Yang, Ming, 2002. "Occupation times and beyond," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 77-93, January.
    11. Dzhaparidze, Kacha & van Zanten, Harry & Zareba, Pawel, 2005. "Representations of fractional Brownian motion using vibrating strings," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1928-1953, December.

    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:13:y:2000:i:3:d:10.1023_a:1007854310936. 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.