IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2010y2010i1n425762.html

Stability of Nonlinear Neutral Stochastic Functional Differential Equations

Author

Listed:
  • Minggao Xue
  • Shaobo Zhou
  • Shigeng Hu

Abstract

Neutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. The well‐known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii‐type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.

Suggested Citation

  • Minggao Xue & Shaobo Zhou & Shigeng Hu, 2010. "Stability of Nonlinear Neutral Stochastic Functional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnljam:v:2010:y:2010:i:1:n:425762
    DOI: 10.1155/2010/425762
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2010/425762
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2010/425762?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
    ---><---

    References listed on IDEAS

    as
    1. Yue Liu & Xuejing Meng & Fuke Wu, 2010. "General Decay Stability for Stochastic Functional Differential Equations with Infinite Delay," International Journal of Stochastic Analysis, Hindawi, vol. 2010, pages 1-17, February.
    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. Wenxue Li & Meng Liu & Ke Wang, 2012. "A Generalization of Itô′s Formula and the Stability of Stochastic Volterra Integral Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

    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.

      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:wly:jnljam:v:2010:y:2010:i:1:n:425762. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

      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.