IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v98y2002i1p23-41.html
   My bibliography  Save this article

Interacting diffusions in a random medium: comparison and longtime behavior

Author

Listed:
  • Greven, A.
  • Klenke, A.
  • Wakolbinger, A.

Abstract

We consider a collection of linearly interacting diffusions (indexed by a countable space) in a random medium. The diffusion coefficients are the product of a space-time dependent random field (the random medium) and a function depending on the local state. The main focus of the present work is to establish a comparison technique for systems in the same medium but with different state dependence in the diffusion terms. The technique is applied to generalize statements on the longtime behavior, previously known only for special choices of the diffusion function. One of these special choices, which we employ as a reference model, is that of interacting Fisher-Wright diffusions in a catalytic medium where duality was used to obtain detailed results. The other choice is that of interacting Feller's branching diffusions in a catalytic medium which is itself an (autonomous) branching process and where infinite divisibility was used as the main tool.

Suggested Citation

  • Greven, A. & Klenke, A. & Wakolbinger, A., 2002. "Interacting diffusions in a random medium: comparison and longtime behavior," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 23-41, March.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:1:p:23-41
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(01)00141-7
    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. Dawson, Donald A. & Fleischmann, Klaus, 1994. "A super-Brownian motion with a single point catalyst," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 3-40, January.
    2. Dawson, Donald A. & Fleischmann, Klaus, 1997. "Longtime behavior of a branching process controlled by branching catalysts," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 241-257, November.
    3. Klenke, Achim, 2000. "Absolute continuity of catalytic measure-valued branching processes," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 227-237, October.
    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. Rüschendorf Ludger & Wolf Viktor, 2011. "Comparison of Markov processes via infinitesimal generators," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 151-168, May.

    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. Klenke, Achim, 2000. "Absolute continuity of catalytic measure-valued branching processes," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 227-237, October.
    2. Mörters, Peter & Vogt, Pascal, 2005. "A construction of catalytic super-Brownian motion via collision local time," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 77-90, January.
    3. Eyal Neuman & Alexander Schied, 2016. "Optimal portfolio liquidation in target zone models and catalytic superprocesses," Finance and Stochastics, Springer, vol. 20(2), pages 495-509, April.
    4. Eduardo Abi Jaber, 2021. "Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02412741, HAL.
    5. Eduardo Abi Jaber, 2021. "Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels," Post-Print hal-02412741, HAL.
    6. Donald A. Dawson & Klaus Fleischmann, 1997. "A Continuous Super-Brownian Motion in a Super-Brownian Medium," Journal of Theoretical Probability, Springer, vol. 10(1), pages 213-276, January.
    7. Eduardo Abi Jaber, 2019. "Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels," Papers 1912.07445, arXiv.org, revised Jun 2020.
    8. Eduardo Abi Jaber, 2020. "Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels," Working Papers hal-02412741, HAL.
    9. Leduc, Guillaume, 2006. "Martingale problem for superprocesses with non-classical branching functional," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1468-1495, October.
    10. Pinsky, Ross G., 2003. "Strong law of large numbers and mixing for the invariant distributions of measure-valued diffusions," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 117-137, May.
    11. Engländer, János & Fleischmann, Klaus, 2000. "Extinction properties of super-Brownian motions with additional spatially dependent mass production," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 37-58, July.
    12. Eyal Neuman & Alexander Schied, 2015. "Optimal Portfolio Liquidation in Target Zone Models and Catalytic Superprocesses," Papers 1504.06031, arXiv.org, revised Jul 2015.

    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:98:y:2002:i:1:p:23-41. 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.