IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v40y1992i1p69-82.html
   My bibliography  Save this article

McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets

Author

Listed:
  • Graham, Carl

Abstract

We consider a 'nonlinear' McKean-Vlasov Ito-Skorohod SDE, and develop a L1 contraction scheme so as to get good results on the non-compensated jumps. We prove existence and uniqueness results under natural Lipschitz assumptions. We show that a wide class of nonlinear martingale problems, giving most diffusions with discrete jump sets, can be represented by SDEs satisfying our L1 assumptions, but not more classical L2 ones. We use this on a probabilistic model for a chromatographic tube. We finish by a propagation of chaos result on sample-paths.

Suggested Citation

  • Graham, Carl, 1992. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 69-82, February.
  • Handle: RePEc:eee:spapps:v:40:y:1992:i:1:p:69-82
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(92)90138-G
    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. Tomoyuki Ichiba & Michael Ludkovski & Andrey Sarantsev, 2019. "Dynamic contagion in a banking system with births and defaults," Annals of Finance, Springer, vol. 15(4), pages 489-538, December.
    2. Benazzoli, Chiara & Campi, Luciano & Di Persio, Luca, 2020. "Mean field games with controlled jump–diffusion dynamics: Existence results and an illiquid interbank market model," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6927-6964.
    3. E. Löcherbach, 2020. "Convergence to Equilibrium for Time-Inhomogeneous Jump Diffusions with State-Dependent Jump Intensity," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2280-2314, December.
    4. Jun Moon & Wonhee Kim, 2020. "Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models," Mathematics, MDPI, vol. 8(10), pages 1-23, September.
    5. Bayraktar, Erhan & Wu, Ruoyu, 2021. "Mean field interaction on random graphs with dynamically changing multi-color edges," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 197-244.
    6. Erny, Xavier, 2022. "Well-posedness and propagation of chaos for McKean–Vlasov equations with jumps and locally Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 192-214.
    7. Benazzoli, Chiara & Campi, Luciano & Di Persio, Luca, 2019. "ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    8. Cecchin, Alekos & Pelino, Guglielmo, 2019. "Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4510-4555.
    9. Dai Pra, Paolo & Formentin, Marco & Pelino, Guglielmo, 2021. "A hierarchical mean field model of interacting spins," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 287-338.
    10. Graham, Carl, 2011. "Convergence of multi-class systems of fixed possibly infinite sizes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 31-35, January.
    11. Yulin Song, 2020. "Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps," Journal of Theoretical Probability, Springer, vol. 33(1), pages 201-238, March.
    12. Tugaut, Julian, 2013. "Self-stabilizing processes in multi-wells landscape in Rd-convergence," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1780-1801.
    13. Detering, Nils & Fouque, Jean-Pierre & Ichiba, Tomoyuki, 2020. "Directed chain stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2519-2551.

    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:40:y:1992:i:1:p:69-82. 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.