IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v73y2005i1p79-90.html
   My bibliography  Save this article

Inequalities for the norms of integrals with respect to a fractional Brownian motion

Author

Listed:
  • Slominski, Leszek
  • Ziemkiewicz, Bartosz

Abstract

Integrals with respect to a fractional Brownian motion with Hurst index for integrands X={Xt;t[set membership, variant][0,T]} with possibly nonregular paths are considered. General inequalities for the norms of such integrals are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:1:p:79-90
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00084-2
    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. 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.
    2. Novikov, Alexander & Valkeila, Esko, 1999. "On some maximal inequalities for fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 47-54, August.
    3. 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.
    4. Kubilius, K., 2002. "The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 289-315, April.
    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, 2018. "Extensions of the sewing lemma with applications," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3940-3965.

    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. 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.
    3. B. L. S. Prakasa Rao, 2021. "Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 554-568, August.
    4. Čoupek, P. & Maslowski, B., 2017. "Stochastic evolution equations with Volterra noise," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 877-900.
    5. Falkowski, Adrian & Słomiński, Leszek, 2017. "SDEs with constraints driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3536-3557.
    6. Axel A. Araneda, 2019. "The fractional and mixed-fractional CEV model," Papers 1903.05747, arXiv.org, revised Jun 2019.
    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. Robert Elliott & Leunglung Chan, 2004. "Perpetual American options with fractional Brownian motion," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 123-128.
    9. Orimar Sauri, 2024. "Asymptotic Error Distribution of the Euler Scheme for Fractional Stochastic Delay Differential Equations with Additive Noise," Papers 2402.08513, arXiv.org.
    10. Salmerón Garrido, José Antonio & Nunno, Giulia Di & D'Auria, Bernardo, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," DES - Working Papers. Statistics and Econometrics. WS 35411, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Alexander Melnikov & Yuliya Mishura & Georgiy Shevchenko, 2015. "Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 169-188, March.
    12. Axel A. Araneda, 2021. "Price modelling under generalized fractional Brownian motion," Papers 2108.12042, arXiv.org, revised Nov 2023.
    13. Davidson, James & Hashimzade, Nigar, 2009. "Representation And Weak Convergence Of Stochastic Integrals With Fractional Integrator Processes," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1589-1624, December.
    14. Nualart, David & Pérez-Abreu, Victor, 2014. "On the eigenvalue process of a matrix fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4266-4282.
    15. Radchenko, Vadym M., 2007. "Besov regularity of stochastic measures," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 822-825, April.
    16. Balan, Raluca M. & Tudor, Ciprian A., 2010. "The stochastic wave equation with fractional noise: A random field approach," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2468-2494, December.
    17. Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
    18. Mahmoudi, Fatemeh & Tahmasebi, Mahdieh, 2022. "The convergence of a numerical scheme for additive fractional stochastic delay equations with H>12," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 219-231.
    19. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    20. León, Jorge A. & Nualart, David, 2005. "An extension of the divergence operator for Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 481-492, 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:stapro:v:73:y:2005:i:1:p:79-90. 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.