IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v2y2000i1d10.1023_a1010059302049.html
   My bibliography  Save this article

Diffusion Processes Associated with Nonlinear Evolution Equations for Signed Measures

Author

Listed:
  • B. Jourdain

    (ENPC-CERMICS)

Abstract

In this paper, we explain how to associate a nonlinear martingale problem with some nonlinear parabolic evolution equations starting at bounded signed measures. Our approach generalizes the classical link made when the initial condition is a probability measure. It consists in giving to each sample-path a signed weight which depends on the initial position. After dealing with the classical McKean-Vlasov equation as an introductory example, we are interested in a viscous scalar conservation law. We prove uniqueness for the corresponding nonlinear martingale problem and then obtain existence thanks to a propagation of chaos result for a system of weakly interacting diffusion processes. Last, we study the behavior of the associated fluctuations and present numerical results which confirm the theoretical rate of convergence.

Suggested Citation

  • B. Jourdain, 2000. "Diffusion Processes Associated with Nonlinear Evolution Equations for Signed Measures," Methodology and Computing in Applied Probability, Springer, vol. 2(1), pages 69-91, April.
    • Handle: RePEc:spr:metcap:v:2:y:2000:i:1:d:10.1023_a:1010059302049
    DOI: 10.1023/A:1010059302049
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1010059302049
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1010059302049?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Shkolnikov, Mykhaylo, 2013. "Large volatility-stabilized markets," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 212-228.
    2. Rémillard, Bruno & Vaillancourt, Jean, 2014. "On signed measure valued solutions of stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 101-122.
    3. BOSSY Mireille & JOURDAIN Benjamin, 2001. "A Stochastic Particle Method For The Solution Of A 1d Viscous Scalar Conservation Law In A Bounded Interval," Monte Carlo Methods and Applications, De Gruyter, vol. 7(1-2), pages 45-54, December.
    4. Tran, Viet Chi, 2008. "A wavelet particle approximation for McKean-Vlasov and 2D-Navier-Stokes statistical solutions," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 284-318, February.
    5. Kolli, Praveen & Sarantsev, Andrey, 2019. "Large rank-based models with common noise," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 29-35.
    6. Jourdain, B., 2000. "Probabilistic approximation for a porous medium equation," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 81-99, September.
    7. Andrey Sarantsev, 2019. "Comparison Techniques for Competing Brownian Particles," Journal of Theoretical Probability, Springer, vol. 32(2), pages 545-585, June.
    8. Shkolnikov, Mykhaylo, 2012. "Large systems of diffusions interacting through their ranks," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1730-1747.

    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:spr:metcap:v:2:y:2000:i:1:d:10.1023_a:1010059302049. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.