IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i8p822-825.html
   My bibliography  Save this article

Besov regularity of stochastic measures

Author

Listed:
  • Radchenko, Vadym M.

Abstract

Let [mu] be a random [sigma]-additive in probability set function defined on Borel subsets of [a,b]. We prove that if the process , has continuous paths, then they belong a.s. to the Besov space for all .

Suggested Citation

  • Radchenko, Vadym M., 2007. "Besov regularity of stochastic measures," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 822-825, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:8:p:822-825
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00015-6
    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. 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.
    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. 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.
    2. Yan, Litan, 2004. "Maximal inequalities for the iterated fractional integrals," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 69-79, August.
    3. 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.
    4. Fan, Xiliang & Yuan, Chenggui, 2016. "Lyapunov exponents of PDEs driven by fractional noise with Markovian switching," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 39-50.
    5. David Nualart & Youssef Ouknine, 2003. "Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2," Journal of Theoretical Probability, Springer, vol. 16(2), pages 451-470, April.
    6. M. Mishra & B. Prakasa Rao, 2011. "Nonparametric estimation of trend for stochastic differential equations driven by fractional Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 101-109, May.
    7. Marie, Nicolas, 2020. "Nonparametric estimation of the trend in reflected fractional SDE," Statistics & Probability Letters, Elsevier, vol. 158(C).
    8. Fan, Xiliang & Yu, Ting & Yuan, Chenggui, 2023. "Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 383-415.
    9. 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.
    10. Radchenko, Vadym, 2019. "Averaging principle for the heat equation driven by a general stochastic measure," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 224-230.
    11. Raluca M. Balan & Ciprian A. Tudor, 2010. "Stochastic Heat Equation with Multiplicative Fractional-Colored Noise," Journal of Theoretical Probability, Springer, vol. 23(3), pages 834-870, September.
    12. Slominski, Leszek & Ziemkiewicz, Bartosz, 2009. "On weak approximations of integrals with respect to fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 543-552, February.
    13. Mishura, Yuliya & Shevchenko, Georgiy, 2017. "Small ball properties and representation results," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 20-36.
    14. 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.
    15. Čoupek, P. & Maslowski, B., 2017. "Stochastic evolution equations with Volterra noise," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 877-900.
    16. 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.
    17. Rang, Guanglin, 2020. "From directed polymers in spatial-correlated environment to stochastic heat equations driven by fractional noise in 1+1 dimensions," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3408-3444.
    18. Fan, Xiliang & Huang, Xing & Suo, Yongqiang & Yuan, Chenggui, 2022. "Distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 23-67.
    19. Lucian Maticiuc & Tianyang Nie, 2015. "Fractional Backward Stochastic Differential Equations and Fractional Backward Variational Inequalities," Journal of Theoretical Probability, Springer, vol. 28(1), pages 337-395, March.
    20. 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.

    More about this item

    Keywords

    Stochastic measures Besov spaces;

    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:77:y:2007:i:8:p:822-825. 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.