IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v89y2000i1p81-99.html
   My bibliography  Save this article

Probabilistic approximation for a porous medium equation

Author

Listed:
  • Jourdain, B.

Abstract

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting diffusion processes. The particle system obtained by increasing reordering from these diffusions is proved to solve a stochastic differential equation with normal reflection. Last, we obtain propagation of chaos for the reordered particles to a probability measure which does not solve the martingale problem but is also linked to the porous medium equation.

Suggested Citation

  • Jourdain, B., 2000. "Probabilistic approximation for a porous medium equation," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 81-99, September.
    • Handle: RePEc:eee:spapps:v:89:y:2000:i:1:p:81-99
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(00)00014-4
    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. 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.
    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. Belaribi, Nadia & Cuvelier, François & Russo, Francesco, 2011. "A probabilistic algorithm approximating solutions of a singular PDE of porous media type," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 317-369, December.
    2. Philipowski, Robert, 2007. "Interacting diffusions approximating the porous medium equation and propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 526-538, April.
    3. Mykhaylo Shkolnikov & Lane Chun Yeung, 2024. "From rank-based models with common noise to pathwise entropy solutions of SPDEs," Papers 2406.07286, arXiv.org.

    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. Shkolnikov, Mykhaylo, 2013. "Large volatility-stabilized markets," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 212-228.
    2. Shkolnikov, Mykhaylo, 2012. "Large systems of diffusions interacting through their ranks," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1730-1747.
    3. 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.
    4. 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.
    5. 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.
    6. Kolli, Praveen & Sarantsev, Andrey, 2019. "Large rank-based models with common noise," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 29-35.
    7. Andrey Sarantsev, 2019. "Comparison Techniques for Competing Brownian Particles," Journal of Theoretical Probability, Springer, vol. 32(2), pages 545-585, June.

    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:spapps:v:89:y:2000:i:1:p:81-99. 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.