IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v118y2008i6p938-951.html
   My bibliography  Save this article

The coding complexity of diffusion processes under Lp[0,1]-norm distortion

Author

Listed:
  • Dereich, Steffen

Abstract

We investigate the high resolution quantization and entropy coding problem for solutions of stochastic differential equations under Lp[0,1]-norm distortion. We find explicit high resolution formulas in terms of the average diffusion coefficient seen by the process. The proof is based on a decoupling method introduced in a former article by the author. Given that link it remains to analyze the coding problem for a concatenation of Wiener processes and to solve the corresponding rate allocation problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:6:p:938-951
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00115-9
    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. 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.
    2. 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.
    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. 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.
    2. Frikha Noufel & Sagna Abass, 2012. "Quantization based recursive importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 287-326, December.
    3. Antoine Jacquier & Louis Jeannerod, 2017. "How many paths to simulate correlated Brownian motions?," Papers 1708.05352, arXiv.org.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

    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:118:y:2008:i:6:p:938-951. 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/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.