IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i5-6p348-356.html
   My bibliography  Save this article

A weak limit theorem for generalized multifractional Brownian motion

Author

Listed:
  • Dai, Hongshuai
  • Li, Yuqiang

Abstract

We provide a result on an approximation to the generalized multifractional Brownian motion in the space of continuous functions on [0, 1]. The construction of this approximation is based on the Poisson process.

Suggested Citation

  • Dai, Hongshuai & Li, Yuqiang, 2010. "A weak limit theorem for generalized multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 348-356, March.
  • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:348-356
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00433-7
    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. Antoine Ayache & Jacques Vehel, 2000. "The Generalized Multifractional Brownian Motion," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 7-18, January.
    2. Enriquez, Nathanaël, 2004. "A simple construction of the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 203-223, February.
    3. Stoev, Stilian A. & Taqqu, Murad S., 2006. "How rich is the class of multifractional Brownian motions?," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 200-221, February.
    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. Hongshuai Dai, 2013. "Convergence in Law to Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 26(3), pages 676-696, September.

    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. Garzón, J. & Gorostiza, L.G. & León, J.A., 2009. "A strong uniform approximation of fractional Brownian motion by means of transport processes," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3435-3452, October.
    2. Ayache, Antoine & Lévy Véhel, Jacques, 2004. "On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 119-156, May.
    3. Loosveldt, L., 2023. "Multifractional Hermite processes: Definition and first properties," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 465-500.
    4. Garcin, Matthieu, 2017. "Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 462-479.
    5. 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.
    6. Anderes, Ethan B. & Stein, Michael L., 2011. "Local likelihood estimation for nonstationary random fields," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 506-520, March.
    7. Loboda, Dennis & Mies, Fabian & Steland, Ansgar, 2021. "Regularity of multifractional moving average processes with random Hurst exponent," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 21-48.
    8. Yu, Z.G. & Anh, V.V. & Wanliss, J.A. & Watson, S.M., 2007. "Chaos game representation of the Dst index and prediction of geomagnetic storm events," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 736-746.
    9. Bojdecki, Tomasz & Talarczyk, Anna, 2012. "Particle picture interpretation of some Gaussian processes related to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2134-2154.
    10. Davidson, James & Hashimzade, Nigar, 2009. "Type I and type II fractional Brownian motions: A reconsideration," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2089-2106, April.
    11. Sergiy Shklyar & Georgiy Shevchenko & Yuliya Mishura & Vadym Doroshenko & Oksana Banna, 2014. "Approximation of Fractional Brownian Motion by Martingales," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 539-560, September.
    12. Balança, Paul, 2015. "Some sample path properties of multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3823-3850.
    13. Peng, Qidi & Zhao, Ran, 2018. "A general class of multifractional processes and stock price informativeness," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 248-267.
    14. Cadoni, Marinella & Melis, Roberta & Trudda, Alessandro, 2017. "Pension funds rules: Paradoxes in risk control," Finance Research Letters, Elsevier, vol. 22(C), pages 20-29.
    15. Biermé, Hermine & Lacaux, Céline & Scheffler, Hans-Peter, 2011. "Multi-operator scaling random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2642-2677, November.
    16. Chen, Zhe & Leskelä, Lasse & Viitasaari, Lauri, 2019. "Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2723-2757.
    17. Mendy, Ibrahima, 2012. "The two-parameter Volterra multifractional process," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2115-2124.
    18. Balança, Paul & Herbin, Erick, 2012. "2-microlocal analysis of martingales and stochastic integrals," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2346-2382.
    19. K. J. Falconer & J. Lévy Véhel, 2009. "Multifractional, Multistable, and Other Processes with Prescribed Local Form," Journal of Theoretical Probability, Springer, vol. 22(2), pages 375-401, June.
    20. Ehsan Azmoodeh & Ozan Hur, 2023. "Multi-fractional Stochastic Dominance: Mathematical Foundations," Papers 2307.08651, arXiv.org.

    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:80:y:2010:i:5-6:p:348-356. 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.