IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v116y2006i2p310-336.html
   My bibliography  Save this article

Functional quantization of a class of Brownian diffusions: A constructive approach

Author

Listed:
  • Luschgy, Harald
  • Pagès, Gilles

Abstract

The functional quantization problem for one-dimensional Brownian diffusions on [0,T] is investigated. One shows under rather general assumptions that the rate of convergence of the Lp-quantization error is like for the Brownian motion. Several methods to construct some rate-optimal quantizers are proposed. These results are extended to d-dimensional diffusions when the diffusion coefficient is the inverse of a gradient function. Finally, a special attention is given to diffusions with a Gaussian martingale term.

Suggested Citation

  • Luschgy, Harald & Pagès, Gilles, 2006. "Functional quantization of a class of Brownian diffusions: A constructive approach," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 310-336, February.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:2:p:310-336
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00126-2
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bonollo, Michele & Di Persio, Luca & Oliva, Immacolata, 2020. "A quantization approach to the counterparty credit exposure estimation," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 335-356.
    2. Dereich, Steffen, 2008. "The coding complexity of diffusion processes under Lp[0,1]-norm distortion," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 938-951, June.
    3. Dereich, Steffen, 2008. "The coding complexity of diffusion processes under supremum norm distortion," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 917-937, June.
    4. Corlay Sylvain & Pagès Gilles, 2015. "Functional quantization-based stratified sampling methods," Monte Carlo Methods and Applications, De Gruyter, vol. 21(1), pages 1-32, March.
    5. Frikha Noufel & Sagna Abass, 2012. "Quantization based recursive importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 287-326, December.
    6. Antoine Jacquier & Louis Jeannerod, 2017. "How many paths to simulate correlated Brownian motions?," Papers 1708.05352, arXiv.org.
    7. Ren'e Aid & Lamia Ben Ajmia & M'hamed Gaigi & Mohamed Mnif, 2021. "Nonzero-sum stochastic impulse games with an application in competitive retail energy markets," Papers 2112.10213, arXiv.org.
    8. Ofelia Bonesini & Giorgia Callegaro & Martino Grasselli & Gilles Pag`es, 2023. "From elephant to goldfish (and back): memory in stochastic Volterra processes," Papers 2306.02708, arXiv.org, revised Sep 2023.
    9. Sagna, Abass, 2011. "Pricing of barrier options by marginal functional quantization," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 371-398, December.
    10. Miranda, Manuel J. & Bocchini, Paolo, 2015. "A versatile technique for the optimal approximation of random processes by Functional Quantization," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 935-958.
    11. Møller, Jan Kloppenborg & Madsen, Henrik & Carstensen, Jacob, 2011. "Parameter estimation in a simple stochastic differential equation for phytoplankton modelling," Ecological Modelling, Elsevier, vol. 222(11), pages 1793-1799.

    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:spapps:v:116:y:2006:i:2:p:310-336. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/505572/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.